Preheat oven to 350 degrees F. Line an 8x8 baking pan or a 9 inch pie pan with parchment paper, leaving overhang on the sides.
In a medium bowl, whisk together flour, baking powder, baking soda, cinnamon and salt, then set aside.
Melt the butter in the microwave or over the stove and place in a large bowl along with the vanilla, granulated sugar and brown sugar. Whisk to combine.
Add eggs to the large bowl with wet ingredients and whisk. Then add reserved dry ingredients to the large bowl of wet ingredients and whisk again.
Peel the apples and grate on the large side of a box grater. Then, add to the large bowl of ingredients and stir until evenly distributed. Put batter into prepared baking pan.
Bake cake until a toothpick comes out clean--around 30 minutes. Let cool before trying to remove from the pan. Enjoy!