In a large bowl, mix the dry ingredients: flour, cocoa powder, sugar, salt, and baking powder.
In a medium bowl, crack the eggs and lightly whisk with the milk and the vanilla extract.
Add the wet ingredients to the dry and stir until just combined.
Then, stir in the cooled, melted butter until combined.
Cover the bowl with plastic wrap, making sure the plastic wrap touches the batter so that it keeps it from drying out (developing a skin over the top). Store in the fridge for 2-12 hours. (Note: I’ve successfully made these up to a day later.)
When you are ready to bake, preheat the oven to 400F.
Brush madeleine molds with a little vegetable oil or spray with cooking spray. Then drop a tablespoon of the dough into each madeleine shell. Be careful not to overfill the shells.
Bake for 8-10 minutes or until done. (In my experience the domes are the very last bit to finish cooking, and you’ll still see wet batter on the tops until they are done.) Remove from oven and allow to cool on a wire rack for a few minutes and then flip them onto a serving plate. They should come out of the tin fairly easy, but if necessary, run a knife around the edges to loosen.