Step 1: Prepare the Cake Batter

1. Preheat Oven: Preheat your oven to 350°F (175°C). Grease and flour a 9×13-inch baking pan.
2. Mix Cake Ingredients: In a large bowl, combine the chocolate cake mix, instant vanilla pudding mix, eggs, milk, vegetable oil, and vanilla extract. Mix until well combined and smooth.

Step 2: Bake the Cake

1. Pour Batter: Pour the chocolate cake batter into the prepared baking pan, spreading it evenly.
2. Bake: Bake in the preheated oven for 30–35 minutes, or until a toothpick inserted in the center comes out clean. Allow the cake to cool in the pan for about 10 minutes, then transfer to a wire rack to cool completely.

Step 3: Make the Cream Cheese Frosting

1. Beat Cream Cheese and Butter: In a medium bowl, beat the softened cream cheese and butter together until smooth and creamy.
2. Add Powdered Sugar: Gradually add the powdered sugar, mixing until well combined.
3. Add Vanilla and Milk: Stir in the vanilla extract and enough milk to achieve a spreadable consistency.

Step 4: Assemble the Cake

1. Frost the Cake: Once the cake has completely cooled, spread the cream cheese frosting evenly over the top.
2. Chill: For best results, refrigerate the cake for at least 30 minutes to set the frosting.

Step 5: Serve

1. Slice and Enjoy: Cut into squares and serve chilled or at room temperature.