Prepare Butter and Apples: Brown butter in a saucepan, then set aside. Sauté peeled and chopped apples with butter and cinnamon for 10 minutes until tender, then cool completely.
Make Blondie Batter: Whisk browned butter and brown sugar. Add eggs and vanilla. In a separate bowl, combine flour, baking powder, salt, cinnamon, and nutmeg. Add dry ingredients to wet and mix until just combined. Fold in cooled apples.
Bake Blondies: Pour batter into a prepared 8x8 or 9x9 inch pan. Bake at 350°F for 35-45 minutes. Cool completely.
Make Frosting: Beat cream cheese and butter. Add powdered sugar, cinnamon, and maple syrup. Beat until light and fluffy.
Frost and Serve: Once blondies are completely cool, spread frosting evenly over the top, slice, and serve.