Preheat oven to 400° F. Grease ten 2 1/2-inch muffin pan cups. In a one-quart saucepan, melt butter. Remove from heat and stir in milk and honey until well mixed. Stir in eggs, set aside.
Meanwhile prepare nut topping by combining the ingredients in a cup. In a large bowl, combine flours, bran, baking soda and salt, set aside. Cut 1/2-inch slice from side of each apple and reserve.
Core and cut enough of remaining apples into 1/4-inch cubes to measure about 1 cup. Fold diced apples into flour mixture. Stir batter mixture into flour mixture just until dry ingredients are moistened. Spoon into greased cups.
Cut reserved apple slices crosswise into 1/8-inch thick slices. Insert 2 or 3 thin slices into top of muffin batter. Sprinkle with nut topping. Bake muffins 20 to 25 minutes or until golden brown. Remove muffins from cups and cool to room temperature on wire rack.Servings: 12 muffins