Preheat oven to 350°F (175°C). Grease three 8-inch round cake pans and line with parchment. Beat 4 eggs and 1 cup sugar until thick and pale, about 5 minutes. Sift flour, baking powder, and salt over the batter, folding gently. Fold in melted butter. Divide among pans and bake 12-14 minutes. Cool 5 minutes in pans, then invert onto a rack to cool completely.

Whisk egg yolks, 1/4 cup sugar, cornstarch, and half the lemon zest. Warm milk until steaming, slowly whisk half into yolks, then return all to saucepan. Cook over medium heat, stirring, until thick and bubbling, 2-3 minutes. Boil 1 minute, remove from heat, stir in 1/4 cup lemon juice and salt. Press plastic wrap onto surface and chill at least 2 hours.

Stir remaining lemon juice, confectioners’ sugar, and remaining zest until sugar dissolves. Brush all of the syrup over cooled cake layers.

Place one soaked layer on a plate, spread with half the lemon cream. Repeat with second layer and remaining cream, top with final layer. Chill 20 minutes.

Whip heavy cream, 2 tbsp confectioners’ sugar, and vanilla to soft peaks. Frost top and sides of cake. Refrigerate at least 1 hour before serving.

Slice and serve cold. Drizzle extra lemon syrup over slices if desired.