Preheat oven to 400 degrees. Butter two madeleine pans; set aside. Sift flour, baking powder, and salt into a bowl; set aside.

Put eggs, egg yolks, granulated sugar, vanilla, and lemon zest and juice in the bowl of an electric mixer fitted with the paddle attachment. Mix on medium-high speed until pale and thickened, about 5 minutes. Mix in butter. Using a spatula, fold flour mixture into egg mixture. Let rest 30 minutes.

Pour batter into buttered pans, filling the molds 3/4 full. Bake cookies, rotating pans halfway through, until edges are crisp and golden, 7 to 8 minutes. Let cookies cool slightly in pans on wire racks. Invert, and unmold. Dust with confectioners' sugar, if desired.

Cookies can be stored between layers of parchment in airtight containers at room temperature up to one day.