Preheat your oven to 350°F (175°C) and line a 12-cup muffin tin with paper liners.

In a medium bowl, whisk together flour, cocoa powder, baking powder, baking soda, and salt until evenly combined.

In a larger bowl, cream the softened butter and granulated sugar together using an electric mixer until light and fluffy, about 3 minutes.

Add eggs one at a time, mixing well after each addition, then stir in the vanilla extract.

In a measuring cup, combine the cooled coffee and milk.

Gradually alternate adding the dry ingredients and the coffee-milk mixture into the butter mixture, starting and ending with the dry ingredients. Mix until just combined.

Divide the batter evenly among the lined muffin cups, filling each about two-thirds full.

Bake for 18–20 minutes, or until a toothpick inserted into the center comes out clean. Allow to cool completely.

Beat the chilled mascarpone cheese with the heavy cream, powdered sugar, cocoa powder, and vanilla extract until stiff peaks form. Add coffee liqueur if using.

Once the cupcakes are completely cool, pipe or spread the mascarpone frosting generously onto each cupcake. Dust with cocoa powder.