Make the quick puff pastry

1. In a large bowl, whisk the eggs with the salt. Stir in the cold water, then add the vinegar and vodka or cognac. Set the mixture aside.
2. Add the flour and cold butter to a food processor. Pulse until the butter breaks down into pea-sized pieces.
3. Pour in the egg mixture and pulse again just until the dough begins to clump together. It should look rough, not smooth.
4. Turn the dough out onto a work surface and gently bring it together with your hands. Work it as little as possible so the butter stays in small pieces. That is what creates the flaky layers later.
5. Divide the dough into 4 equal portions. Shape each piece into a ball, flatten slightly into a disk, wrap well, and chill for 1 to 2 hours. You can also refrigerate it for several days if making ahead.

Make the egg yolk custard

1. In a large 6-quart pot, whisk the egg yolks and sugar together. Add a little milk if needed to loosen the mixture. Whisk in the flour until smooth and lump-free, adding a splash more milk if necessary.
2. Heat the remaining milk in a saucepan over medium heat until hot and steaming, or boil it gently in the microwave if you prefer.
3. Slowly stream the hot milk into the egg mixture while whisking constantly to temper it.
4. Return the mixture to the pot and cook over medium heat, whisking nonstop, until it comes to a boil and thickens. Continue cooking for 2 to 3 minutes, or until the custard no longer tastes floury.
5. Stir in the vanilla and butter until fully melted and smooth.
6. If needed, strain the custard through a fine sieve to remove any lumps.
7. Transfer the custard to a rimmed baking sheet and cover it with plastic wrap pressed directly onto the surface to prevent a skin from forming. Let it cool. If making ahead, refrigerate it covered for up to 3 days.

Bake the pastry layers

1. Preheat the oven to 400°F and position a rack in the center.
2. Flip a 12 x 16-inch baking sheet upside down and place it on a damp kitchen towel so it does not slide while you roll the dough.
3. Take one chilled dough ball and cut it in half. Roll each half into a very thin 12 1/2-inch circle on the back of the baking sheet, dusting lightly with flour as needed.
4. Prick the dough all over with a fork every 1 to 2 inches so it bakes evenly.
5. Bake for 5 to 7 minutes, or until lightly golden. These layers bake fast, so keep an eye on them.
6. The moment each layer comes out of the oven, place an 11-inch plate, lid, or stencil on top and trim it into a neat round with a sharp knife or pizza cutter. Save the scraps in a separate bowl.
7. Repeat until you have 8 baked layers total.
8. Crumble the scraps into fine crumbs and set them aside for the outside of the cake.

Assemble the cake

1. Divide the custard into 8 roughly equal portions. As it cools, it will thicken, which makes it easier to portion.
2. Place a small dab of custard on the serving plate, then add the first pastry layer and press gently to secure it.
3. Set a cake ring around the first layer and fasten it with a ribbon or cake strip if you have one. This is optional, but it helps keep the edges tidy.
4. Spread one portion of custard evenly over the layer. Repeat with the remaining layers and custard, ending with some custard on top.
5. Scatter a layer of cake crumbs over the top so the custard does not dry out.
6. Carefully run a thin knife between the cake and the ring, then remove the ring.
7. Spread the remaining custard around the sides in an even layer, then press the remaining crumbs onto the sides until fully coated. Add any leftover crumbs to the top.
8. Gently tap the plate to shake loose extra crumbs, clean the edges, and chill the cake until ready to serve.