Preheat oven to 350°F. Prepare a 10-cup Bundt pan by greasing or spraying with nonstick coating. Set aside.
Combine the cake mix, pudding, oil, water, eggs, applesauce, apples, cinnamon baking chips, and cinnamon with a hand mixer. Pour into the prepared Bundt pan.
15.25 ounces yellow cake mix, 6.8 ounces instant vanilla pudding, ½ cup vegetable oil, 1 cup water, 4 large eggs, 1 cup unsweetened applesauce, 1½ cups diced apples, ¾ cup cinnamon baking chips, 1 tablespoon ground cinnamon
Bake 40-45 minutes. To check for doneness, insert a toothpick into the middle of a section of cake. If it comes out clean, it's done.
Let the cake cool on the counter for about 10 minutes. Then, invert cake onto a serving plate and lift off the pan to finish cooling.
For the icing, combine the cream cheese, butter, milk, cinnamon, powdered sugar, and vanilla in a mixing bowl. Using a hand mixer, beat until fluffy.
¼ cup unsalted butter, 4 cups powdered sugar, 3 tablespoons milk, 1 tablespoon ground cinnamon, 1 teaspoon pure vanilla extract, 8 ounces cream cheese
Once the cake is fully cooled, spread with icing and sprinkle with more cinnamon chips, if desired.