Combine cracker crumbs and melted butter in a bowl. Mix until evenly moistened; press into the bottom and sides of a 9x13-inch baking dish.
Bake in preheated oven until crust is lightly browned and smells toasted, about 15 minutes. Remove from the oven and cool.
Mix ice cream, pudding mix, and milk together in a bowl until combined; spread evenly onto prepared crust. Spread whipped topping over ice cream mixture; top with toffee bits. Place in freezer until hardened, at least 1 hour.