Cream butter and sugars in a mixer for 1-2 minutes. Add in egg and vanilla and combine. In a separate bowl, combine flour, baking powder, salt, and cocoa; add to butter mixture and mix on low setting. While the mixer is on low, pour in milk and coffee; combine. If the batter is too runny, add a small amount more of flour. Be careful not to overmix; turn off the mixer once the batter is smooth.
Use an ice cream scoop to fill a greased or lined cupcake pan. This recipe will make 12 cupcakes, so fill the tins accordingly. Bake for 15-18 minutes until an inserted toothpick comes out clean. Remove from pan and let cool on a baking rack.
While cupcakes are cooling, beat the butter in a mixing bowl (I used a hand mixer). Add in powdered sugar one cup at a time, beating each cup in until it resembles frosting. Add cream, vanilla, and salt, and then beat until the frosting is thick and creamy. I like to beat this for a couple minutes, as it whips air into the frosting and creates a nice volume. Frost your cupcakes as desired - I used a Wilton 1M decorating tip.