Preheat oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking pan.
Combine cream cheese, sugar, and banana in a large bowl; beat with an electric mixer on medium speed until well blended. Add eggs one at a time, mixing batter well after each addition. Fill graham cracker crust with batter. Reserve remaining batter in the bowl.
Bake cheesecake in the preheated oven until middle is set and top is pale yellow, 30 to 40 minutes. Chill until firm.
Pour chocolate cake mix, water, applesauce, and vegetable oil over the remaining batter in the bowl; mix well. Pour into the greased baking pan.
Bake in the preheated oven until top springs back when lightly pressed, 30 to 40 minutes. Cool completely before slicing.