Preheat the oven to 350 degrees F. Lightly spray the sides and bottom of a 9-inch springform pan with nonstick baking spray. Press a parchment paper strip that is 3 inches tall along the greased sides. It will stick up above your pan.
In a large bowl, add in the cream cheese. Beat with a hand mixer on medium until smooth.
Add in the sugar and flour and continue to beat until incorporated.
Add in the vanilla extract and then the eggs one at a time. Beat in each egg just until incorporated before adding the next egg. Scrape down the sides and bottom of the bowl. Beat in any bits that need to be incorporated.
Cake
Add the red velvet cake mix, water, oil, and eggs into a large mixing bowl. Beat with a hand mixer until incorporated and smooth.
Assemble
Divide the red velvet cake batter in half. Spread the first half of the batter into the bottom of the prepared pan.
Divide the cheesecake batter in half. Using a large spoon, dollop the first half of the cheesecake batter on top of the cake batter. Don't spread or swirl the cheesecake batter.
Slowly add the remaining red velvet cake batter by the spoonfuls around the cheesecake batter. Do not spread the cake batter.
Add the remaining cheesecake batter on top of the other 3 layers.
Spread this batter using an offset spatula into an even layer.
Place in the oven and bake at 350 degrees for 50-60 minutes or until the center is set and when a toothpick is inserted into the center of the cake, it comes out clean. If the cheesecake appears to be browning too fast make a foil tent to cover the top for the last 20-30 minutes. The cheesecake will puff up in the oven and the cake may also crack but after it is cooled it will settle.
Remove from the oven.
Transfer the cheesecake to a wire rack to cool to room temperature.
Once cooled, place in the refrigerator to set up overnight.
Before serving, add the cream cheese frosting to the cheesecake cake.
Frosting
Add the cream cheese and butter to a medium mixing bowl. Beat using a hand mixer on medium until smooth.
Gradually add in the powdered sugar and continue to mix until well combined.
Add in the vanilla extract and milk and beat until incorporated.
Release the ring of the springform pan.
Spread the cream cheese frosting evenly on top of the cake with an offset spatula.
Sprinkle the crushed candy canes on the edge
Cover and refrigerate the cheesecake until it is ready to be served.
Notes
If the cheesecake appears to be browning too fast make a foil tent to cover the top for the last half of the bake time.
The cheesecake will puff up in the oven and the cake may crack but after it is cooled it will settle.