For the madeleine cakes:

1. In a large glass measuring cup, melt 8 tablespoons of butter in the microwave. Place a paper towel on top in case you get distracted and let it go too long. 
2. In the bowl of a stand mixer fitted with the whisk attachment, beat the eggs and sugar on high for at least 10 minutes. The mixture should be thick and pale yellow. Check if it’s done by using a spoonful of batter and drizzling it in a figure 8. If it stays for a few seconds, it’s done. Next, add the vanilla and beat again until combined.
3. Carefully fold the dry ingredients (flour, cocoa powder, baking powder, and salt) into the wet ingredients and with a rubber spatula, stir the wet and dry ingredients until combined. Don’t overmix; it will take all the air out of the batter, and you won’t have light, fluffy little cakes.
4. Add the melted butter and mix until combined. The batter should have a sheen to it.
5. Transfer the batter to a smaller bowl, cover tightly with plastic wrap, and place it in the refrigerator for at least 1 hour and up to 2 hours.
6. Preheat the oven to 350 degrees. Spray the madeleine pan with cooking spray and using the pastry brush, make sure all the crevices are coated. Alternatively, you can brush the wells of the pan with melted butter. Some of the cakes stick to the pan when I’ve used butter which is why I use cooking spray.
7. Take the batter out of the refrigerator and don’t stir or mix. It will deflate the batter.
8. Using a medium cookie scoop, fill the scoop with the batter and scrape off any excess. Place the ball of batter in the center of each well of the madeleine pan. It will spead evenly to fill the mold while baking.
9. Place the madeleine pan in the middle of the oven rack and bake for 5 minutes. Rotate the pan and bake for another 5 minutes. Remove the pan from the oven, let the madeleines cool in the pan for a few minutes, and then turn the madeleines out of the pan and onto the cooking rack.

For the dipping chocolate:

1. Chop the chocolate into pieces and place them in a heat-proof or microwave safe bowl.
2. Place the bowl in the microwave and melt the chocolate in 15-second increments. Stir the chocolate after each heating session and continue until the chocolate is melted. Be careful not to go too long as the chocolate can burn and become bitter.
3. Let the melted chocolate cool for a few minutes.
4. After the madeleines have reached room temperature, dip the end of each one, at an angle, in the chocolate and set it on the cooling rack. Sprinkle a little sea salt on the chocolate-dipped end and let the chocolate set. If you’re in a hurry, you can place the dipped madeleines in the refrigerator.