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

In a medium bowl, sift together flour, cocoa powder, baking powder, baking soda, and salt. Whisk to combine.

In a separate small bowl, stir together the milk, ½ cup coffee, and vanilla extract.

In a stand mixer, cream the softened butter and sugar until light and fluffy, about 3-4 minutes.

Add eggs one at a time, mixing well after each addition. Mix in the melted dark chocolate.

With mixer on low, add dry ingredients in three parts, alternating with the coffee-milk mixture in two parts. Mix until just combined.

Divide batter evenly among the 12 muffin cups. Bake for 18-22 minutes, or until a skewer comes out clean.

While cupcakes bake, make the soak: stir warm coffee, liqueur, and sugar until sugar dissolves.

As soon as cupcakes are out of the oven, poke holes in the tops with a skewer. Generously brush with the coffee soak.

Let cupcakes cool completely in the pan on a wire rack.

For the frosting, whip cold mascarpone, cold heavy cream, powdered sugar, and vanilla on medium-high speed until stiff peaks form.

Frost the cooled cupcakes. Refrigerate for at least 2 hours (or overnight) before dusting with cocoa powder and serving.