Preheat the oven to 350 F/175 C. Line a cupcake tin. Set aside.
Melt the butter and chocolate together in a double boiler on the stove. This may be accomplished by putting a Pyrex bowl over a pot of simmering water (don't let the bowl touch the water). Stir until smooth. Set aside to slightly cool.
In a medium-sized bowl, toss the cocoa powder, flour, baking soda, baking powder, and salt together until combined.
In another bowl, beat the eggs, sugar, brown sugar, and vanilla together until smooth. Add the cooled butter/chocolate mixture and beat until smooth. Add half of the flour mixture, then half of the buttermilk, alternating until everything has been incorporated. Stir until just combined; do not over mix.
Divide the batter into the cupcake liners. Bake for 18 minutes, or until a toothpick inserted in the center comes out clean. Allow to cool completely before frosting.