Preheat oven to 350℉, and prepare a 9-inch cake pan by greasing the sides with nonstick cooking spray, or butter, and lining the bottom with parchment paper
In a large bowl, beat the softened butter with an electric mixer until smooth
Add in the granulated sugar and brown sugar and mix until combined, light and fluffy
Beat in the vanilla extract, ground cinnamon, nutmeg, eggs and milk until combined
Add in the all purpose flour, baking powder and salt, and beat until just combined
Using a rubber spatula, gently fold in the diced apples
Evenly spread the batter in prepared cake pan
Make the cinnamon sugar topping by combining the granulated sugar and cinnamon together in a small bowl
Sprinkle cinnamon sugar mixture on top of the cake
Bake for 35 minutes, or until cake is golden brown, the edges of the cake are pulling away from the pan, and a toothpick comes out clean
Remove from oven and allow to cool completely