Preheat oven to 180 °C (356 °F) and place a rack in the center. Prepare a madeleine pan or muffin tin so the cakes won't stick (use a non-stick or greased pan or silicone molds).
Ensure the 100 g of melted chocolate has cooled until warm to the touch but not hot so it will not cook the eggs.
In a large bowl, beat the 100 g room-temperature butter and 100 g sugar until pale and creamy (about 2–3 minutes with an electric mixer).
Add the 3 eggs one at a time, mixing until each is incorporated. Stir in the 1 tbsp vanilla extract.
Mix the cooled melted chocolate into the batter until evenly combined.
In a separate bowl, sift together the 150 g flour, 10 g baking powder, and a pinch of salt.
Gently fold the dry ingredients into the wet ingredients until just combined and the batter is soft and airy. Do not overmix.
Spoon the batter into the prepared madeleine or muffin cups, filling each about three-quarters full to allow room for rising.
Bake at 180 °C (356 °F): 10–15 minutes for madeleine molds, or 15–20 minutes if using regular muffin cups. They are done when the tops are golden and spring back lightly or a skewer inserted into the center comes out clean.
Remove from oven, let the pieces sit in the pan 1–2 minutes, then transfer to a wire rack to cool. Cool completely before serving.