Add the eggs and sugar to the bowl of a stand mixer fitted with the paddle attachment. Beat on medium-high speed until smooth, pale yellow, and creamy, about 8-10 minutes. Stir in the vanilla.
2 large eggs, ½ cup granulated sugar, 1 teaspoon pure vanilla extract
In a separate bowl, combine the flour, cocoa powder, and baking powder. Gently fold into the egg mixture.
¾ cup all-purpose flour, ¼ cup unsweetened cocoa powder, ½ teaspoon baking powder
Fold in the melted butter.
½ cup unsalted butter
Transfer the batter to the refrigerator for about 1 hour (I don’t usually cover mine but use plastic wrap or a kitchen towel if you prefer to cover it).
Towards the end of the chilling step, preheat the oven to 350°F and grease a madeleine pan with melted butter or nonstick cooking spray.
Scoop the batter into the molds until they are ¾ full. Gently press the batter into the molds (wetting your hand helps prevent the batter from sticking).
Bake until the madeleines are light brown, about 13 minutes.
Transfer the madeleines to a wire rack to cool.
If desired, garnish with a light dusting of powdered sugar or dip in melted chocolate.