Combine first 5 ingredients in a large bowl. Combine egg whites, oil, and vanilla in a small bowl; stir into dry ingredients. Spread batter in a 9-inch square baking pan coated with cooking spray. Bake at 350° for 22 minutes. Cool completely in pan on a wire rack.
Line an 8 x 4-inch loaf pan with plastic wrap. Spread chocolate ice cream in bottom of pan. Spread coffee ice cream over chocolate ice cream. Cut brownie into 2 equal pieces. Place one piece over ice cream in pan. Reserve remaining brownie for another use. Cover pan with plastic wrap and freeze at least 4 hours.
Combine fudge topping and liqueur in a small saucepan. Cook over medium heat until sauce is warm. Spoon about 1 tablespoon sauce onto each dessert plate.
Remove terrine from freezer. Remove top sheet of plastic wrap. Invert terrine onto a platter; remove remaining plastic wrap. Cut terrine into 1/2-inch slices. Place 1 slice over sauce on each plate.