Preheat oven to 325°.
Combine hot water and 2 teaspoons coffee granules in a bowl; stir well. Add 2 cups brownie mix, 1 teaspoon vanilla, and egg whites; stir until well-blended. Pour mixture into a 9-inch pie plate coated with cooking spray. Bake at 325° for 22 minutes (brownie will be fudgy when tested with a wooden pick). Let cool completely on a wire rack.
Combine milk, 2 tablespoons Kahlúa, 1 teaspoon coffee granules, 1 teaspoon vanilla, and pudding mix in a bowl; beat at medium speed of a mixer 30 seconds. Gently fold in 1 1/2 cups whipped topping. Spoon pudding mixture into brownie crust; spread evenly.
Combine 1 tablespoon Kahlúa and 1 teaspoon coffee granules in a bowl; stir well. Gently fold in 1 1/2 cups whipped topping. Spread whipped topping mixture evenly over pudding mixture. Garnish with chocolate curls, if desired. Serve immediately or store loosely covered in refrigerator.
Note: Nonalcoholic Mocha Version: When making the pudding mixture, substitute 2 tablespoons 1% low-fat milk for the Kahlúa. In the topping omit the Kahlua and dissolve the instant coffee granules in 1 tablespoon water.
Note: Store remaining brownie mix in a heavy-duty, zip-top plastic bag in refrigerator; use mix to make another pie or a small pan of brownies. To make brownies, combine about 2 cups mix, 1/4 cup water, and 1 lightly beaten egg white in a bowl. Stir just until combined. Spread in an 8-inch square pan coated with cooking spray. Bake at 350° for 23 to 25 minutes.