In a large bowl, combine the flour, sugar, baking powder, salt, cinnamon and nutmeg. In another bowl, whisk the egg, milk, oil and applesauce. Stir into dry ingredients just until moistened. Fold in apple. Fill greased or paper-lined muffin cups half full.
For topping, in a small bowl, combine brown sugar and flour; cut in butter until crumbly. Add oats. Sprinkle over muffins.
Bake at 350° for 18-22 minutes or until a toothpick inserted in the center comes out clean. Cool for 5 minutes before removing from pan to a wire rack.
In a small bowl, beat the butter, honey and cinnamon until blended. Serve with warm muffins. Refrigerate leftover butter.