Place rack in the middle of the oven and heat to 350°F. Lightly coat a 9x13-inch baking pan with cooking spray; set aside.
Blend 1 cup of oats in a blender or food processor until a fine powder forms, about 30 seconds. Transfer the flour to a medium bowl. Add the remaining oats, cinnamon, baking powder, and salt and stir to combine.
Place the applesauce, eggs, and maple syrup in a large bowl and whisk to combine. Add the oat mixture and stir to combine.
Transfer the batter to the prepared baking pan and spread into an even layer. Sprinkle the apple pieces over the top, lightly pressing them into the batter.
Bake until golden-brown and a toothpick inserted in the center comes out clean, about 20 minutes in a metal pan, or up to 30 minutes in a glass or ceramic pan. Transfer the pan to a wire rack to cool completely. Cut into squares and serve.