Preheat oven to 350 degrees. Grease and flour a bundt pan and set aside.
Add flour, baking powder, baking soda, cinnamon, clove, ginger, nutmeg, and sea salt and whisk together until uniform in appearance.
In another bowl, combine brown sugar, pumpkin puree, milk, butter, eggs, and vanilla extract until uniform.
Add wet ingredients to dry ingredients and stir until just combined and no dry pockets remain. Peel and shred apple then mix into cake batter.
Transfer batter to prepared bundt pan and bake on center oven rack for about 45 minutes or until a toothpick inserted into multiple parts of the cake comes out clean. Cool for about 10 minutes in pan then remove and allow to cool completely.
For the Maple Cream Cheese Frosting
Meanwhile, beat powdered sugar, cream cheese, butter, maple syrup, and vanilla extract until fluffy, glossy, and uniform (about four minutes). Frost cooled cake as desired.