1. Preheat oven to 350 F with the rack in the middle.
2. Spray a 12-cup bundt pan with nonstick cooking spray with flour.

To make the filling:

1. Add the mascarpone, butter, and sugar in a bowl. Using an electric hand mixer, beat on medium speed until well combined and smooth. Add the eggs, flour, cinnamon, and vanilla beating just until incorporated. Set aside.

To make the cake:

1. Add the flour, sugar, cinnamon, salt, baking soda, baking powder, cinnamon and nutmeg and whisk. Add the eggs, oil, applesauce, and vanilla, and mix just until using a sturdy spoon. Fold in the apples until evenly distributed.
2. Spoon 1/3 of the cake batter into the prepared pan. Top evenly with 1/2 of the cheesecake filling, leaving a 1-inch border around the edge of the pan. This is easiest if you spoon it in instead of pouring it. Try your best to not have it touch the sides of the pan.
3. Use a thin, long-blade knife to swirl the cheesecake filling with the cake batter just a few times. Don’t overdo it. Top with another 1/3 of the batter and the rest of the cheesecake filling. Stick the knife in only about an inch and swirl again. Top with the remaining cake batter.
4. Bake for 55-65 minutes, or until a cake tester inserted in the center of the cake comes out clean. Transfer the pan to a wire rack and cool for 15-20 minutes.
5. Place another wire rack on top and grasping the rack with the edges of the pan, gently invert the cake onto the rack and allow to cool completely ~at least 2-3 hours.

To make the frosting:

1. Place milk and flour in a medium saucepan over medium heat. Whisk continuously until the mixture begins to bubble lightly and the mixture thickens. After about 7 minutes the mixture should be the consistency of thick cake batter. Remove from the heat, add in the vanilla bean seeds, stir, and set aside to cool completely.
2. Once the mixture has cooled completely (THIS IS IMPORTANT!), in the bowl of a stand mixer fitted with the whisk, add the butter and sugar and beat on high until light and fluffy and almost white, ~ 3 minutes. The sugar should be completely incorporated into the butter. Stop the mixer and add the cooled milk mixture to the butter mixture. Beat on high until all ingredients are incorporated, about 1 minute. The texture should resemble whipped cream. At this point, you can spread on top of the cake or if you want a drizzle consistency add a few tablespoons of cream or milk to the frosting to thin it out slightly.