Preheat the oven to 350° F. Line an 8-inch by 8-inch pan with parchment paper and set aside.
In a medium bowl, whisk together flour, baking powder, salt, cinnamon and nutmeg. Set aside.
In a large bowl, whisk together melted butter and brown sugar until well combined, about 2 minutes. Add egg and vanilla and mix until incorporated. Add the flour mixture and stir just until combined (careful not to overmix). Fold in chopped apples.
Transfer batter to prepared baking pan (the batter will be a little thick). Bake for 25 to 28 minutes or until a toothpick inserted into the center comes out clean. Cool and cut into squares and serve.
*Nutritional information is an estimate. Please consult a doctor or nutritionist for the most accurate nutritional info.