Prepare 16x12x1-inch sheet pan (half sheet) by lightly greasing or spraying with non-stick cooking spray.
Cut open one end of pouch and squeeze batter into prepared pan.
Spread batter with spatula until even.
For convection oven, bake at 325°F 27-32 minutes; for standard oven, bake at 375°F 36-41 minutes.
Brush warm brownies with brewed coffee. Allow brownies to cool completely before cutting.
Beat mascarpone, vanilla, rum, and powdered sugar with mixer on medium speed until smooth. Fold whipped topping into mascarpone mixture.
Place brownie on serving dish. Pipe mascarpone-rum mousse on top of the brownie in desired design. Sift or sprinkle cocoa over the top. Drizzle with a thin stream of ganache to garnish.