Preheat oven to 400°F. Insert paper liners in muffin tins, set aside.
In a large bowl, combine the bran, whole wheat flour, baking soda, baking powder, salt, brown sugar, and walnuts and stir until well mixed.
Measure the oil and yogurt into the blender (or processor) and add the banana, broken up. Blend at medium speed until uniform, then pour over the dry ingredients. Stir gently until all is wet.
Spoon the batter into the foil liners and bake for about 20 minutes.