Beat the eggs with the sugar, vanilla and half of the milk until thick and light yellow. Add the flour and baking powder bit by bit and continue mixing until smooth. Stir in the rest of the milk and the melted butter.
Carefully grease your madeleine tray if necessary. Spoon about two tablespoons of batter into each mold. Bake for 15 minutes at 375°F. Cool on a rack.
Makes 24 madeleines.
You could flavor your madeleines with different things, perhaps orange or lemon zest. A dusting of powdered sugar would look nice as well.