Whisk eggs, milk, flour, melted butter, sugar, salt, and vanilla until the batter is smooth and the consistency of heavy cream; strain through a fine sieve to remove lumps.

Cover and rest the batter in the refrigerator for 30 minutes, which relaxes the gluten so the crepes stay thin and tear-resistant.

Heat a lightly buttered 9-inch nonstick skillet over medium heat. Pour in 1/4 cup batter, swirling to coat the bottom in a thin, even layer.

Cook each crepe for about 45 seconds, until the edges lift and the underside turns pale gold, then flip and cook 20 seconds more. Stack cooked crepes on a plate; you need about 20 for a tall cake.

Make the pastry cream: whisk egg yolks, sugar, and cornstarch in a bowl until pale. Heat the milk in a saucepan until it just steams, then pour slowly into the yolk mixture, whisking constantly.

Return the mixture to the saucepan and cook over medium heat, whisking constantly, until it thickens to the consistency of pudding and coats the back of a spoon, 3 to 4 minutes.

Remove from heat, stir in vanilla and butter, then press plastic wrap directly onto the surface and chill for 1 hour, until fully cold.

Fold the whipped cream into the cold pastry cream in two additions to lighten it into a spreadable cream.

Lay one crepe on a cake stand and spread a thin, even layer of cream to the edges, about 2 tablespoons per layer.

Repeat with the remaining crepes and cream, stacking straight and pressing gently every few layers to keep the sides even, ending with a plain crepe on top.

Refrigerate the finished cake for at least 2 hours, until the layers are firm enough to slice cleanly.

Just before serving, dust the top with torn gold leaf and scatter pomegranate arils around the edge.