Preheat oven to 400 degrees F. Grease a 12-cup muffin tin, or line with cupcake papers.
Mix together the flours, brown sugar, baking soda, baking powder, cinnamon, and salt. Once mixed, add oats and cranberries, and stir well. Add the egg, oil, milk, carrots, and banana, and stir just until blended.
Drop batter into prepared muffin tin, about 1/4 cup of batter in each. Bake in preheated oven about 23-25 minutes. Check for doneness by inserting a toothpick into the center of a muffin. If the toothpick comes out clean, the muffins are done. Serve warm or at room temperature.