In a bowl, mix the eggs and sugar until foamy. Add the vanilla, mix some more.
Sift the flour and make sure there are no lumps.
Incorporate the butter. Mix well. Use a hand mixer if you prefer.
Add the baking power and mix.
Allow the preparation to rest in the fridge for 30 min to an hour.
Preheat the oven at 420F (or 220C)
Put one tablespoon of the mixture in each madeleine mold and place in the oven at 420F (220C) for 6 minutes and drop the temperature to 350F (180C) and bake another 6 minutes.
Take out of the oven and allow to cool.