Preheat the oven to 425 degrees F (220 degrees C). Grease a baking sheet.
Whisk both flours, white sugar, baking powder, baking soda, and salt together in a bowl. Cut in butter with 2 knives or a pastry blender until mixture resembles coarse crumbs. Stir in blueberries and walnuts. Beat yogurt and banana in a small bowl until smooth; add to flour mixture and stir gently just until dough holds together.
Turn dough out onto prepared baking sheet and pat into an 8-inch circle. Score the dough into 8 wedge-shaped pieces using a butter knife. Sprinkle brown sugar evenly over dough.
Bake in the preheated oven until lightly browned, 18 to 20 minutes.
While scones are baking, whisk confectioner's sugar and water together in a small liquid measuring cup. Drizzle over warm scones before serving.
Nutritional Facts
Per 8 servings
Calories: 249
Carbohydrate: 40g
Fat: 9g
Fiber: 2g
Protein: 5g
Sugar: 17g
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