Preheat oven to 375°F. Lightly coat twelve 2-1/2-inch muffin cups with nonstick cooking spray or line with paper bake cups and coat insides of paper cups with nonstick cooking spray; set aside. In a large bowl stir together all-purpose flour, whole wheat flour, the 1/3 cup brown sugar, the baking powder, apple pie spice, and salt. Make a well in the center of the flour mixture; set aside.
In a medium bowl lightly beat eggs with a fork; stir in buttermilk and oil. Add egg mixture all at once to flour mixture; stir just until moistened (batter should be lumpy). Fold in shredded apple. Spoon batter into prepared muffin cups, filling each about three-fourths full.
In a small bowl combine pecans, flaxseed meal, and the 1 tablespoon brown sugar. Using a pastry blender, cut in butter until mixture resembles coarse crumbs. Spoon pecan mixture on top of muffin batter.
Bake for 18 to 20 minutes or until a toothpick inserted in centers comes out clean. Cool in muffin cups on a wire rack for 5 minutes. Remove muffins from muffin cups. Serve warm.