Preheat the oven to 375°F. Grease and flour a 12-cup muffin pan, or line with papers and grease the insides of the papers., Mix together the butter, granulated sugar, and 1/4 cup of the brown sugar, beating until fluffy., Add the egg and mix well, stopping once to scrape the sides and bottom of the bowl., Gently mix in the buttermilk or yogurt., Stir in the flours, baking powder, baking soda, salt, and cinnamon., Fold in the chopped apples., Divide the batter evenly among the prepared muffin cups, sprinkling the remaining 1/2 cup brown sugar on top., Bake the muffins for 25 to 30 minutes, or until a toothpick inserted into the center of a muffin comes out clean., Remove the muffins from the oven, cool them for 5 minutes in the pan, then turn them out onto a rack to finish cooling completely.