In a medium bowl (that's heat safe) add the chocolate, butter and cocoa powder and set over a medium saucepan of simmering water. Do not let the bowl touch the water or let the water come to a boil. Stir frequently until melted and smooth and set aside.
In a mixer fitted with the whisk attachment (see mixer Notes below recipe), add the eggs, sugar, brown sugar, vanilla, peppermint extract and salt and whisk on medium-high for about 5 to 7 minutes or until thick and light in color. Add in the melted chocolate (no need to let it cool) and run the mixer for 30 seconds on low to combine. Fold in the flour until just combined (make sure there aren't any flour pockets). Pour the brownie batter into the prepared baking dish.
Bake the brownies in the center of the oven for 15 minutes and then sprinkle the tops of the brownies with the peppermint dust (reserving the bigger bits of peppermint to garnish the finished brownies). Return the brownies to the oven and continue baking for 10-12 minutes (for a total of 25 to 27 minutes bake time).
When done, the tops will be puffed with some cracks and if you test with a toothpick some crumbs will cling to it. Let on a wire rack and let the brownies cool in the pan for about 30 minutes and then transfer to the fridge to cool completely for 1 to 2 hours.