Make puff pastry dough: In a bowl whisk eggs and salt, stir in water, vinegar. Pulse flour and cold butter in food processor until pea‑sized crumbs form, then add egg mixture and pulse until dough just comes together. Gather lightly by hand—do not overwork.

Divide dough into 4 pieces, flatten into disks, wrap and refrigerate for 1–2 hours.

Prepare egg‑yolk custard: Whisk sugar and yolks, adding a splash of milk as needed for smoothness. Whisk in flour to make lump‑free batter. Heat remaining milk to a simmer, temper it into yolk mixture, then return to heat, whisking constantly until thickens and boils for 2–3 minutes. Remove from heat, stir in vanilla and butter until smooth. Strain if needed, spread onto a rimmed sheet pan and cover with cling film touching surface to prevent skin. Let cool to room temperature.

Bake pastry layers: Preheat oven to 400 °F (200 °C). Remove dough one disk at a time, cut each into two portions. Roll each thinly (≈12½ in circle) on lightly floured surface or inverted baking sheet. Prick all over with fork. Bake 5–7 min until lightly golden. Immediately cut circles (≈11 in) using plate as stencil, reserve scraps and crumble. Repeat until you have eight layers.

Assemble cake: Spread a bit of custard on serving plate, place first layer and press to adhere. Use cake ring or ribbon if desired. Spread 1/8 of custard over each layer, stacking layers. Use half of remaining custard on top. Crumble pastry scraps over top and press into sides. Gently tap cake to unsettle crumbs.

Refrigerate, or serve within 3 hours to enjoy crisp‑flaky texture. For soft, tender result, cover and refrigerate for 24–48 hours before serving.