Preheat oven to 375 degrees F. Line a baking sheet with foil or parchment paper; set aside. In a medium bowl combine flours, oats, sugar, baking powder, and salt. Using a pastry blender, cut in butter until mixture resembles coarse crumbs. Make a well in the center of the flour mixture; set aside.
In a medium bowl combine sour cream and egg white. Stir in 3/4 cup of the chocolate chunks. Add sour cream-chocolate mixture all at once to flour mixture. Using a fork, stir just until moistened.
Turn out dough onto a lightly floured surface. Knead by folding and gently pressing dough for 10 to 12 strokes or until dough is nearly smooth. Pat or lightly roll dough into a 10-inch circle. Cut into 12 wedges.
Place wedges 1 inch apart on the prepared baking sheet. Bake for 18 to 20 minutes or until edges are just starting to brown.
Meanwhile, place the remaining 1/4 cup chocolate chunks in a small microwave-safe bowl. Microwave on 50 percent power (medium) for 1 minute. Stir; microwave on 50 percent power (medium) for 30 to 60 seconds more or until melted and smooth, stirring once. Cool slightly.
Drizzle melted chocolate over warm scones. Serve scones warm.