Napoleon Cake (Russian Mille-Feuille)

Method

1. 1Grate the cold butter on a coarse grater straight into the flour and toss to coat. This keeps it cold and avoids warming it with your hands. Mix the egg, cold water, vinegar, and salt and drizzle into the flour-butter crumbs. Fold until it barely holds together — don't knead. Divide into 10–12 balls, wrap, and refrigerate at least 2 hours.
2. 2Roll each portion directly on a sheet of baking paper into a very thin round or rectangle (about 2 mm). Prick all over with a fork. Bake one or two at a time at 200°C for 7–10 minutes until golden. Cool completely on a rack. Set one layer aside for the crumb topping.
3. 3Make the custard: whisk the egg yolks, sugar, and vanilla sugar until pale. Whisk in the flour. Warm the milk almost to a boil, then pour it in a thin stream into the egg mixture, whisking constantly. Return to the heat and stir until thick and bubbling — about 5 minutes. Take off the heat.
4. 4Cool the custard to about 40°C, then beat in the softened butter a little at a time until it's glossy and smooth. Press film onto the surface and cool to room temperature.
5. 5Place the first pastry layer on a serving board. Spread a generous layer of custard. Repeat with all remaining layers, pressing each one gently to level. Finish with custard on the top and sides.
6. 6Crumble the reserved layer into fine crumbs and press them all over the top and sides.
7. 7Refrigerate at least 6 hours — overnight is better. The layers must fully absorb the cream before slicing. Serve cold.