Line a rimmed 12-by-8 1/2-inch baking pan with parchment paper. Spray the paper with nonstick cooking spray and set aside.
In a large bowl, use a rubber spatula to stir together the brownie mix, eggs, liqueur, vegetable oil and almond extract. Spread the mixture evenly over the prepared baking pan. Bake until the brownie is just set, 18 to 20 minutes. Cool in the pan for 10 minutes before removing to a wire rack to cool completely.
Line a 9-by-5-inch loaf pan with a piece of parchment paper across the short way, so there is about 2 inches of overhang on either side. Remove the ice cream from the freezer to soften just slightly.
Place the brownie sheet on a cutting board and cut into 3 rectangles. Place one brownie on the bottom of the prepared loaf pan. Scoop the softened vanilla ice cream on top of the brownie and spread evenly with an offset spatula. Place another brownie rectangle on top of the ice cream and press down gently. Scoop the softened chocolate-chocolate chip ice cream on top and spread evenly. Top with the last brownie, press firmly, and wrap in plastic wrap. Freeze for at least 5 hours or preferably overnight.
To unmold, run a thin knife along the two short sides of the pan to loosen. Invert the cake onto a chilled plate. Peel off the parchment and dust the cake with the confectioners' sugar if using. If desired, line the sides with the mini candy canes. Return the cake to the freezer to set for 10 minutes. Slice and serve.