Preheat oven to 375F. Grease 12 muffin cups or coat with cooking = spray. In a medium-sized mixing bowl, beat eggs. Stir in = buttermilk, molasses, oil, grated apple, and mashed banana.
Measure bran, flour, sugar, baking powder, baking soda, and cinnamon = into a large mixing bowl. Stir with a fork until mixed, then, make a = well in center. Pour in fruit mixture, stirring just until combined. = Stir in blueberries or cranberries.
Immediately spoon batter into muffin cups. Bake in center of 375F = oven until golden and a cake tester inserted into center of a muffin = comes out clean, about 30 minutes. Remove from oven and let stand = for 5 minutes. Then turn out onto a cooling rack. Serve warm. Store = muffins in a sealed bag at room temperature for up to 2 days. For = longer storage, refrigerate muffins or preferably freeze.