Bake the brownies in a 9×9 baking dish, according to the instructions.
Cool fully on a wire rack. Allow the ice cream to sit at room temperature for 30 minutes, until soft enough to spread, but not melted.
Spread the ice cream into an even layer overtop the cooled brownies. Freeze for 1 hour, then spread the whipped cream over top. Cover and freeze for 4 to 6 hours, until set.
Sprinkle the peppermints over top and drizzle with melted chocolate. Cut into squares and serve cold.
*The cake will keep in the freezer, tightly covered, for up to 6 months.