For the Cake:

1. Preheat your oven to 350°F (175°C) and grease a 9×13-inch baking pan.
2. In a mixing bowl, whisk together the dry ingredients: flour, baking powder, baking soda, cinnamon, and salt.
3. In a separate bowl, combine the wet ingredients: applesauce, sugar, eggs, vegetable oil, and vanilla extract.
4. Gradually fold the dry ingredients into the wet mixture, stirring gently until just combined. Do not overmix.
5. Pour the batter into the prepared pan and spread it evenly.
6. Bake for 30-35 minutes, or until a toothpick inserted into the center comes out clean.
7. Allow the cake to cool completely before applying the frosting.

For the Cinnamon Cream Cheese Frosting:

1. In a mixing bowl, beat together the softened cream cheese and butter until smooth and creamy.
2. Gradually add the powdered sugar, one cup at a time, and continue mixing until fully incorporated.
3. Mix in the ground cinnamon and beat until the frosting is fluffy and smooth.
4. Spread the frosting evenly over the cooled cake using a spatula.