Line a 9x13 inch pan with foil and let foil extend at least 1 inch over edges of pan. Bake brownies according to package instructions. Cool completely and place in freezer to chill.
Soften ice cream, either by letting it sit at room temperature and stirring every 10 minutes, or by heating at half power in the microwave until you can stir it easily with a spoon. It should be the consistency of frosting. Gently spread evenly over brownies. Place pan in freezer to chill while you prepare the next step.
Place chocolate chips in a bowl. Heat cream in microwave until hot and bubbly. Pour cream over chocolate and cover bowl with plastic wrap. Let sit 5 minutes and then whisk until smooth. Whisk in peppermint extract and let chocolate mixture cool almost in room temperature. Drizzle evenly over ice cream in pan. Sprinkle crushed cookies evenly over chocolate and lightly press in with your hands. Spread whipped topping in an even layer over all. If desired, sprinkle shaved or curls chocolate, or sprinkles on top.
Freeze at least several hours (an up to several days, covered), until firm. When ready to serve, let sit at room temperature about 10-15 minutes to soften. Remove entire dessert from pan by picking up foil edges. Cut into squares and serve.