Preheat oven to 400°.
Lightly spoon flour into dry measuring cups; level with a knife. Combine flour, baking powder, sugar, salt, and pepper in a large bowl; cut in butter with a pastry blender or 2 knives until mixture resembles coarse meal. Stir in cheese and ham. Combine buttermilk and egg whites, stirring with a whisk. Add to flour mixture, stirring just until moist.
Turn dough out onto a lightly floured surface; knead lightly 4 to 5 times with floured hands. Pat dough into an 8-inch circle on a baking sheet coated with cooking spray. Cut dough into 8 wedges, cutting into but not through dough. Bake at 400° for 20 minutes or until lightly browned.