In a small bowl, whisk together the eggs, water, vinegar, and salt. Set aside.

In a food processor, combine flour, salt, and cold butter. Pulse until crumbly. Transfer to a large bowl, add the egg mixture, and mix until a dough forms. Knead on a lightly floured surface until smooth. Divide into 10–12 equal pieces, shape into balls, cover with plastic wrap, and refrigerate for 1 hour.

In a bowl, whisk egg yolks, sugar, and cornstarch until smooth. In a saucepan, heat milk until hot but not boiling.

Gradually pour the hot milk into the egg mixture while whisking constantly. Pour the mixture back into the saucepan and cook over medium-low heat, stirring, until thickened (about 7–8 minutes).

Remove from heat, stir in butter and vanilla until smooth. Cover with plastic wrap and let cool completely.

Preheat the oven to 375°F (190°C).

On parchment paper, roll each chilled dough ball into a very thin circle. Use an 8-inch (20 cm) cake ring or pan to trim each layer. Prick with a fork. Keep the dough scraps on the tray.

Bake layers for 10–12 minutes until lightly golden. Repeat for all layers (you can bake two at a time on one tray). Cool completely. Save the baked scraps for garnish.

Place the first layer on a serving plate. Spread about 3 tablespoons of cream over it. Repeat the process until all layers are stacked. Cover the top and sides with the remaining cream.

Place the baked dough scraps in a food processor and blend into fine crumbs. Press the crumbs onto the top and sides of the cake.

Refrigerate the cake overnight before serving.