Cut butter into chunks, and place in small saucepan along with the chopped chocolate.
Heat over low, stirring frequently, until both butter and chocolate are melted. Set aside to cool.
Combine eggs and sugar in a med-large bowl.
Using an electric mixer, beat eggs with sugar for about 2 minutes, until mixture has thickened and has roughly doubled in size.
With a sifter or fine-meshed sieve, add flour, cocoa powder, baking powder, and salt to the bowl.
Stir until well-combined, then stir in vanilla extract and melted butter/chocolate mixture.
Spray madeleine pan with cooking spray and put in the freezer for 15 minutes. Put the batter in the refrigerator to chill during this time. Preheat the oven to 400 degrees Fahrenheit.
Remove pan from the freezer and fill each mold with a rounded tablespoon of batter—the amount should look like it would fill ¾ of each mold if spread out.
Bake for 9 minutes, and remove when madeleines spring back if you touch them gently.
Bang tray on the counter gently when you remove it from the oven, then wait a minute or two and carefully remove the madeleines onto a cooling rack.
Let cool, and sprinkle with powdered sugar to serve.
Notes
Expert Tips: In the first step, make sure you use a heavy pan and heat gently so as to not scorch the chocolate or brown the butter.If you don’t have cooking spray, you can use butter or olive oil to grease the molds before chilling and then adding the batter. Greasing the molds really helps quite a bit with removing the madeleines cleanly. Note that you may be tempted to flour the molds after greasing them, but this results in an unattractive white film on the chocolate madeleines.It may seem fussy, but the 15 minute step of chilling the batter and the mold is necessary for getting the traditional madeleine “bump” on the top of the cakes. However, don’t leave the batter to chill for much longer or it won’t spread out much at all when you bake it. This is different from a traditional madeleine, where you can chill the batter for much longer.Storage Tips: Madeleines are best the day they are made; however, they will keep for 2-3 days at room temperature or refrigerated in an airtight container. If you choose to refrigerate them (giving the madeleines a longer shelf life), you should bring them to room temperature before serving, and wait to sprinkle with powdered sugar until ready to serve. You can freeze them as well, for up to 2 months.