Prepare and bake brownies according to package directions, using an 8×8 pan for thicker brownies, or 9×13 pan for thinner. Cool brownies completely.
Set ice cream out on a countertop for 30 minutes to soften. (You want it soft enough to spread over brownies but still slightly frozen)
Once ice cream is softened, spread it evenly over the top of the brownies. Cover tightly with saran wrap and foil. Place in freezer and freeze for at least 6 hours or overnight.
Slice ice cream brownie bars into squares, using a sharp knife that’s been run under hot water. Serve each slice with drizzles of caramel and chocolate sauce. Top each with pieces of cookie dough.