Preheat oven to 350 degrees F (175 degrees C). Grease two 8-inch round pans.
Mix cake mix, water, eggs, and oil together in a bowl until well blended. Pour batter into the prepared pans.
Bake in the preheated oven until a toothpick inserted into the center of a cake comes out clean, 26 to 31 minutes. Cool in pans for 10 minutes. Turn cakes out onto clean dishcloths. Let cool for 30 minutes.
Mix confectioners' sugar and sour cream together in a bowl until well blended. Add whipped topping; mix well. Cover with plastic wrap and refrigerate icing for at least 30 minutes.
Place 1 cake layer on a serving plate. Trim top until flat. Spread a thin layer of icing on top. Spread the cheesecake filling on the cake to about 1/2-inch from the edge of the cake. Cover with second cake layer; frost entire cake with the remaining icing.
Place chocolate chips in a small bowl.
Bring heavy cream to a boil in a small saucepan. Remove from heat; let cool for 1 minute. Pour over the chocolate chips. Add vanilla extract; stir until smooth. Pour immediately on top of the cake, letting some of the mixture slide down the sides of the cake. Refrigerate until ready to serve.