Preheat oven to 350°. Line a baking sheet with parchment paper, and set aside.
Combine flour, oats, brown sugar, baking powder, baking soda, and salt in a food processor. Process 10 seconds or until oats are finely chopped. Add butter; process until mixture resembles coarse meal.
Transfer flour mixture to a large mixing bowl; stir in cherries and crystallized ginger.
Combine buttermilk and egg whites in a small bowl; stir with a whisk. Add buttermilk mixture to flour mixture; stir just until a sticky dough forms.
Transfer dough to parchment paperlined baking sheet, and pat into a 9-inch circle (about 1-inch thick). Sprinkle with all-purpose flour, if necessary, to keep the dough from sticking to hands. Divide the dough into 8 equal wedges. Separate wedges slightly, and bake at 350° for 25 minutes or until golden brown and a wooden pick inserted in center comes out clean.