Step 1: Preheat your oven to 350°F (175°C). Prepare the red velvet cake mix according to the package instructions.
Step 2: Pour the cake batter into a greased 9x13 inch baking pan and bake for about 25-30 minutes, or until a toothpick comes out clean. Allow to cool completely.
Step 3: In a separate bowl, combine ricotta cheese, cream cheese, sugar, and vanilla extract. Use an electric mixer to beat until smooth. Add instant cheesecake pudding mix and cold milk, mixing until thickened.
Step 4: Cut the cooled cake in half horizontally. Spread half of the cheesecake filling on one layer, place the second layer on top, and spread the remaining filling on top.
Step 5: Spread Cool Whip over the cheesecake filling. Optionally, decorate with sprinkles or chocolate shavings.
Step 6: Cover with plastic wrap and refrigerate for at least 4 hours, or overnight. Slice and serve chilled.