Preheat oven to 350° F. Lightly grease a 9 x 13-inch pan.
Melt butter in a large skillet over medium heat. Once butter is melted, add apple pieces, sugar, and 1 tsp cinnamon. Cook until apples slightly soften (about 3-5 minutes). Remove from heat and set aside.
In a medium size bowl, whisk together flours, remaining cinnamon, baking powder, baking soda, and salt.
In a large mixing bowl, beat eggs, oil, and sugars until pale. Stir in milk and vanilla.
Add dry ingredients to egg mixture. Mix until just combined.
Gently fold in apples. Pour batter into prepared pan. Arrange apple slices over batter.
Bake 25-30 minutes, or until a toothpick inserted into the center comes out clean (a couple of crumbs are fine!)
Make the glaze by whisking powdered sugar, maple syrup, and milk until well combined. Pour glaze over warm cake.