For the madeleines: Melt the butter in a small saucepan over low heat. Beat the eggs with the sugar in a bowl until pale, about 5 minutes. Add the lemon zest and juice and the vanilla. Stir in the flour and baking powder, and then the melted butter. Butter and flour two 12-cookie madeleine molds. (Traditionally, these have the shape of small shells.) Pour the batter into the molds, filling them three-quarters of the way. Refrigerate for at least 2 hours. Preheat the oven to 425 degrees F (220 degrees). Bake the madeleines for 5 minutes, then turn down the oven temperature to 350 degrees F (180 degrees C) and bake until golden brown and puffed in the center, about 10 minutes more. For the lemon glaze: Mix the confectioners' sugar and lemon juice in a bowl. Before serving, dip the top of each madeleine in the lemon glaze. Garnish with lemon zest. Cook's Note: Letting the batter rest in the refrigerator and then baking them at a high temperature will help the madeleines rise.