Heat oven to 350 degrees. Line a 13x9-in baking pan with foil, letting foil extend about 2 inches above the pan at both ends. Coat foil with nonstick spray.
Spread cake batter in prepared pan. Bake as box directs. Cool completely in pan on a wire rack. Holding he foil ends, lift from the pan. Trim rounded top off cake with a long serrated knife until flat. Holding foil ends. lift cake and return cake to pan.
Mix 1/4 cup of expresso and the liqueur in a small bowl until blended. Brush over top of the cake.
Stir mascarpone and remaining expresso in a large bowl until blended. Beat cream and sugar in a medium bowl on high speed until soft peaks form when beaters are lifted. Fold into cheese mixture until smooth. Spread over cake, adding swirls with the back of a spoon.
Lightly dust cake with cocoa stirred through a strainer. Cut into squares; cut squares diagonally in half. Garnish with coffee beans, if desired.