In a large mixing bowl, combine ½ cup melted unsalted butter, 1 cup brown sugar, ⅓ cup cocoa powder, and 1 teaspoon vanilla extract. Stir until well-blended. Add room-temperature egg and ½ cup chilled mascarpone cheese, mixing until smooth.

Gradually add 1 cup all-purpose flour, ½ teaspoon baking soda, ½ teaspoon baking powder, and a pinch of kosher salt to the wet mixture. Stir until just combined and chill the dough for 30 minutes.

Preheat oven to 350°F. Scoop 1 tablespoon of dough, roll into balls, and place on lined baking sheet. Bake for 9 minutes, reshape if necessary after removing from oven.

Dissolve 1 teaspoon espresso powder in 1 teaspoon vanilla extract. Beat ½ cup room temperature butter until smooth, then add 2 cups sifted powdered sugar and espresso-vanilla mixture, mixing until fluffy. Fold in ½ cup mascarpone cheese.

Pair cookies by size, pipe frosting on one cookie, and top with another. Refrigerate for 30 minutes to allow frosting to set.