Preheat the oven to 450°F. Grease and flour 18 muffin cups and set aside.
Mix together the flours, baking powder, baking soda, salt,nutmeg and cinnamon, and set aside. In a separate bowl, cream the butter and add the granulated sugar and 1/4 cup of the brown sugar. Beat until fluffy. Add the egg and mix well; stop once to scrape the sides and bottom of the bowl.Mix in the buttermilk gently. (If you over-mix, the buttermilk will cause the mixture to curdle.) Stir in the dry ingredients and fold in the apple chunks.
Divide the batter evenly among the prepared muffin cups, sprinkling the remaining 1/4 cup brown sugar on top. Bake for 10 minutes, turn the heat down to 400°F, and bake for an additional 5 to 10 minutes, or until a toothpick inserted into the center of a muffin comes out clean. Cool the muffins for 5 minutes in the tin, then turn them out onto a wire rack to cool completely.