Position a rack in the center of the oven and preheat to 375 degrees F. Line 12 (1/2-cup) muffin cups with paper liners.
Whisk flours, oat bran, baking powder, baking soda, and salt in a medium bowl.
Lightly beat the eggs and egg white in a medium bowl. Stir in the buttermilk, brown sugar, and oil. Stir the liquid mixture into the flour mixture until just evenly moist; the batter will be very thick. Fold in the dried fruit. Divide the batter evenly among the muffin cups. Top with the walnuts. Bake until firm when pressed gently, about 25 minutes. Turn the muffins out of the cups and cool on a rack; serve warm or room temperature.
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