Preheat your oven to 190°C (375°F).
Grease your madeleine pan with butter or cooking spray.
In a microwave-safe bowl, melt the chocolate in short bursts, stirring until smooth. Allow it to cool slightly.
Whisk together the eggs and sugar until light and frothy (3-5 minutes with an electric mixer).
Stir in the vanilla extract and slightly cooled melted chocolate until combined.
Sift together the flour, baking powder, and salt in another bowl.
Gently fold the dry ingredients into the egg and chocolate mixture using a spatula.
Add the softened butter and gently fold until just combined.
Spoon the batter into the prepared madeleine pan, filling each mold about 3/4 full.
Bake for 10-12 minutes, until edges are golden and a toothpick comes out clean.
Allow to cool in the pan for a few minutes before gently removing.
