Preheat the oven to 350°F Line 12 cupcake molds or muffin tins with paper liners or spray with nonstick spray. To make the cupcakes, sift together the flour, cocoa, baking soda and salt. Mix in the chocolate chip. In a medium bowl, whisk together the egg, brown sugar, and white sugar. Whisk in the milk, coffee, and melted butter. Whisk in the dry ingredients. Divide the batter evenly among the cupcake molds, filling them about three-quarters full.
Bake for 15 minutes, or until a tester inserted in the middle of teh cupcakes comes out clean. Cool for 10 minutes. Using a small spatula or knife, remove the cupcakes from the pan. Continue to cool on a wire rack to room temperature.
To make the frosting, melt together chopped chocolate, heavy cream and butter in the microwave oven, until smooth. Let sit until it reaches a spreading consistency, about 1 hour. Spread the frosting on top of the cupcakes.