Prepare the brownie mix as directed on package, adding in the vanilla. Reserve 1 cup of the batter. Spread the remaining batter in greased 9-inch square baking pan.
Beat the cream cheese, flour, and sugar in a medium bowl with an electric mixer on medium speed until smooth. Add the Irish cream liqueur, egg, and food coloring; beat until well blended. Pour the batter over the brownie layer in the pan. Drop the reserved 1 cup batter by spoonfuls over the cream cheese layer. Cut through the batter with a knife several times to create a marble effect.
Bake as directed on the brownie package for a 9-inch square baking pan. Cool in the pan on a wire rack, then cut into squares. Serve with a small scoop of vanilla ice cream, if desired.
