Unprovable Opéra

Shop the ingredients in advance. This reciPL is very hard, and very expensive. Be prepared for non-trivial proofs, and possibly unprovable lemmas.

We’ll state this reciPL through 5 lemmas. First, we identify the premises (a.k.a ingredients). Make sure you have a kitchen scale, a mixer, a blender. You’ll also need a cake pan (with removable bottom) 40cm x 30cm, baking paper, luck and patience.

Ingredients

• 670g unsalted butter (I am not joking)
• 20 eggs (I am sorry, I am not joking part 2)
• 520ml 3% milk
• 380g regular white sugar
• 340g almond flour
• 340g icing sugar (don’t use regular sugar here, you’ll need this special type of sugar)
• 300g dark chocolate
• 90g white flour
• 2 tbsp Illy coffee (please use a decent coffee)
• 3 tbp Illy instant coffee
• Water (we’ll specify the measures in the description of the lemmas)
• 75ml heavy cream 35%
• 35g cocoa powder
• 1 tbsp (15ml) liquid glucose
• 1 gelatin sheet (yes, this exists!)

Preparation - it hurts

This is probably the most difficult reciPL I have ever executed. I might have executed it 8 times, and I miserably failed in my first 2 attempts. But now I think I reached a somewhat stable provable state, so let me share the lemmas with you:

Lemma biscuit: 

Melt 70g of butter in low heat. Let it cool down.

Pre-heat your oven to 220C.

Bowl1 Using the kitchen scale, weight the empty large bowl you are about to use. Take note of it’s weight. You’ll thank me later when it’s time to split this content in 3 parts… In the bowl, sift the almond flour, then the white flour, then the icing sugar (this is commutative). It’s time for adding 8 eggs. Mix it all with a mixer (hopefully you’ll have a stand mixer - otherwise you’ll also do a lot of exercise to hold your portable mixer, like me). The end result must be some homogeneous foundation. Add the butter (which should be cool by now). Mix it again.

Bowl2 Take another bowl, add 9 egg whites (reserve 5 egg yolks). Mix them for a while, until you see a few bubbles coming up. Split 50g of white sugar in 3 portions (I know, it’ll never be exactly equal due to floating point arithmetic, but make an approximation). Add the first third to the egg whites, mix it all up. Add the second portion of sugar, gently mix it. Add the last portion, mix it until you see a fairly homogeneous mix.

Gently add half of the content of Bowl2 in the Bowl1, mix it very gently with a wire whisk, from the bottom to the top. Add the other half, mix it very, very gently.

Weight the final result. Remember I asked you to weight the empty bowl1? Obtain the weight of the final mix. Cover your cake pan with baking paper, add exactly 1/3 of the mix in it. Make sure it covers all the bottom surface. Do you have multiple cake pans and they all fit into your oven? Lucky day! If you bake the 3 biscuits in parallel, the result will be superb because the egg whites will hold their air… (It’s not my case and I have to bake one by one).

Bake the biscuits for 7-10 minutes. They must be slightly golden at the top. Once you remove the cakes from the oven, cover them with plastic wrap. Don’t wait until they cool down! Cover them while they are warm. Make sure you use a safe food wrap for the matter. Set them aside while you prove the next lemmas.

Proof.
Admitted.

Lemma coffee:

Prepare 250ml of Illy coffee (use 2 tbsp of coffee). You’ll need to put sugar in it - 40g. This proof is very easy.

Proof.
Admitted.

Lemma butter_cream:

Pan1 Add 300ml of milk in a low heated pan. Add 3 tbsp of Illy instant coffee (you can use another brand… I can’t just guarantee provability if you change the terms). Let it boil. Set the pan aside, let it cool down while you execute the next step.

Pan2 In another pan, add 5 egg yolks and sift 50g of white sugar on top of it. Mix it all. Slowly, Add the coffee-milk content from the pan. Mix it all, slowly.

Take Pan2 to low heat. Using a silicone spatula, keep mixing it until it becomes a cream (it’ll be ready when it easily gets out of your spatula). When it reaches this point, mix it with a mixer, until it cools down a bit. Add 500g of cold, unsalted butter (Add 100g each, you’ll have 5 batches). Keep the mixer on all the time. You’ll end up with a very heavy cream. Set it aside.

Pan3Bowl1 Take 3 egg whites to glass bowl. Sift 90g of white sugar on top of it. Put water on the bottom of the pan, put the bowl over the pan. Take it to low heat (bain marie), mix it until the sugar dissolves completely. Once it’s done, take it out of the heat, and mix it with a mixer until you reach an uniform mix.

Take the content of the bowl1 (the result of the previous paragraph), mix the half of it with the contents of Pan2. Mix it all using your mixer (which, at this point, must be exhausted). Then repeat for the other half. Set it aside.

Proof.
Admitted.

Lemma choco_ganache:

Another easy proof!

Add 300g of chocolate in a bowl.

Boil 220ml of milk. Put it in the bowl with chocolate. Let it sit for approx 5 minutes. Mix the contents. Add 100g of cool, unsalted butter. Mix it all with a wire whisk. Set it aside.

Proof.
Admitted.

Theorem gateau_build:

It’s time to build the foundational layers of our cake.

Remove the plastic wrap of the biscuits. Be EXTREMELLY GENTLE when removing the baking sheet. Anything can ruin the proof now (a.k.a. break the biscuits). We don’t want that. Add the one of the biscuits in that 40cm x 30cm cake pan with removable bottom. Use the results of Lemma coffee to moist the biscuit layer. Be generous with the coffee amount. Add half of the butter_cream on top of it. Spread it all over the surface. Make it as even as possible. Cover it with food wrap, put in the freezer for 15-20min.

Get back the cake pan, add the second biscuit. Repeat the process to make it moist with coffee. Add all the choco_ganache. Spread it all over the surface. Make it as even as possible. Cover it with food wrap, put in the freezer for 15-20min. (It is a recursive process that terminates, I guarantee).

Get back the cake pan, add the last layer of biscuit. Add the other half of butter_cream. Spread it all over the surface. Make it as even as possible (seriously, try your best in this top layer). Cover it with food wrap, put in the freezer for 30-40min.

Is it over? NO!

Proof.
Admitted.

Lemma choco_frosting_top:

Let’s make a quick chocolate frosting for the top, final layer of this cake.

Hidrate the gelatin sheet.

Pan1 Sift 100g of white sugar, 75ml of heavy cream, 45ml of water. Sift 35g of cocoa powder. Add the liquid glucose. Mix it all, let it boil. Let if cool down until 50C.

Remove the water of the gelatin sheet, add it into Pan1 Mix it all. You can use your mixer if it’s still alive. Let it cool until it reaches 30C.

Proof.
Admitted.

Theorem opera:

Get the main body of the cake out of the freezer, remove the food wrap.

Pour the frosting you built on the previous step on top of the cake. Hint: use a large strainer to remove any air bubbles from the frosting. It will make it super shiny.

Get a sharp knife, pass it on the borders of the cake pan. Remove the bottom.

It is ready!!

Qed.

Now it’s time to enjoy this beautiful and tasty artifact!

Useful hints

Follow the typing rules. Seriously.

Save the egg yolks; you can make cream custard with them, and fill delicious buns. I can post the reciPL in another opportunity.

Appendix, Types and Artifact

The authors are very tired after this submission.

Fun fact: I completed another artifact of these before sending out this reciPL. It took me good 5h or baking, building and cleaning. We need a CI for this reciPL.

• 2022 2
• 2021 14