Preheat oven to 325 degrees F (165 degrees C). Grease a 9x13-inch baking pan.
Combine brownie mix, eggs, water, and oil in a large bowl; stir until well blended. Spread mixture evenly into prepared pan.
Bake in preheated oven until top is dry and edges have started to pull away from the sides of the pan, 20 to 25 minutes. Cool completely, about 30 minutes. Cut into 1-inch squares.
Beat cream cheese in a large bowl with an electric mixer. Add milk and pudding mix; beat until smooth. Fold in whipped topping until well incorporated into filling.
Place 1/2 of the brownie squares at the bottom of a trifle bowl or glass serving dish; top with filling. Shave 1/2 of the chocolate bar onto filling using a vegetable peeler. Repeat with remaining brownies, filling, and chocolate bar shavings. Refrigerate until set, about 1 hour.