Heat oven to 400°F. Lightly coat a large baking sheet with nonstick cooking spray.
Combine flour, 1/2 cup of the sugar, baking powder, baking soda, salt and nutmeg in a large bowl. Add butter; cut in with a pastry blender or 2 knives until mixture resembles coarse crumbs. With a fork, stir in buttermilk, apple and cheddar pieces just until mixture forms a dough.
Turn dough out onto floured surface. Knead 6 or 7 times. Divide dough in half and gather each into a ball. Pat each portion into a 6- to 7-inch circle; place on coated baking sheet. Using sharp knife coated with nonstick cooking spray, cut each round into 6 equal wedges. Brush with egg white; sprinkle with remaining 2 teaspoons sugar.
Bake in 400°F oven for 20 to 25 minutes or until golden brown and no longer soft in the center. With a serrated knife, cut through earlier wedge marks. Remove to rack to cool. Serve warm or at room temperature.