Special equipment: two 12-cup muffin tins; cupcake liners; a candy thermometer
For the cupcakes: Preheat the oven to 350 degrees F. Line the cups of two 12-cup muffin tins with cupcake liners.
Whisk together the flour, baking powder, salt and baking soda in a medium bowl.
Put the chocolate in a microwave-safe bowl and microwave, stirring every 30 seconds, until melted, about 1 1/2 minutes (or melt it in a double boiler).
Put the granulated sugar, brown sugar and butter in the bowl of a stand mixer and beat until light and fluffy, about 3 minutes. Add the melted chocolate and beat to combine. Add the eggs one at a time, beating well after each addition. Beat in the vanilla. Add the flour mixture in 3 batches, alternating with the milk, and beat on low until just combined.
Divide the batter evenly among the cupcake liners, about 1/4 cup batter in each. Bake until the cupcakes are domed slightly and a toothpick inserted into the center comes out clean, about 18 minutes. Cool completely on a rack.
For the icing: Make the icing right before you are ready to frost the cupcakes. Combine the granulated sugar, buttermilk, butter, baking soda and vanilla in a medium to large heavy-bottomed saucepan (the liquid will double in volume). Insert a candy thermometer, bring to a boil and boil over medium-high heat until the mixture reaches soft-ball stage (235 degrees F), 10 to 15 minutes. Remove from the heat as it hits the soft-ball stage to avoid over caramelizing.
Working very quickly but carefully, pour the caramel into the bowl of a stand mixer and beat on medium-high speed until cooled to warm, about 5 minutes. Working quickly, spoon about a tablespoon of the caramel icing onto each cupcake. (Caramel hardens a little as it cools; whip in a splash of heavy cream to loosen it up if needed.) Let stand until set, about 5 minutes. Decorate with edible silver dragees.