For the cupcakes:
Center the oven rack in the middle and preheat the oven to 350 F (180 C).
Line a 12-cup muffin tin with paper liners.

Combine the flour, cocoa, baking powder, sodium bicarbonate, and salt. Set aside.

Beat the butter and sugar until smooth.
Add the egg, then the egg yolk, mixing well between each addition, then add the vanilla and mix.
Reduce the speed of the electric mixer, then incorporate the reserved dry ingredients in alternation with the buttermilk.
Incorporate the melted chocolate and mix well.

Divide the dough into each muffin cup and bake for 22 to 25 minutes.
Let cool for 5 minutes in the pan before transferring to a rack to cool completely.

For the frosting:
Melt the chocolate in a double boiler, then transfer the bowl to the counter and let cool for 5 minutes.
Using a whisk, incorporate the powdered sugar, then the butter.
Let cool completely before frosting the cupcakes.