Combine the mascarpone, 1/2 cup confectioners' sugar, the coffee liqueur and vanilla in a large bowl and beat with a mixer on medium speed until creamy, about 1 minute (do not overmix).
Combine the heavy cream and 1/4 cup confectioners' sugar in a separate bowl; beat on medium-high speed until stiff peaks form. Fold the whipped cream into the mascarpone mixture in 3 additions; set aside.
Combine the espresso and the remaining 1 tablespoon confectioners' sugar in a shallow bowl. One at a time, dip 12 doughnut halves in the espresso mixture and arrange in a single layer in a 9-by-13-inch baking dish, breaking the doughnuts as necessary to cover the bottom of the dish.
Spread one-third of the mascarpone mixture over the doughnuts. Dip the remaining 12 doughnut halves in the espresso mixture and arrange on top. Spread the remaining mascarpone mixture on top. Cover with plastic wrap and refrigerate at least 4 hours or overnight. Cut into pieces and dust with cocoa powder.