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.