Preheat oven to 400 degrees. Line a muffin pan with papers. Shred carrots and mash ripe banana.
In a large bowl, whisk together flour, brown sugar, baking soda, baking powder, nutmeg, and salt until there are no lumps. Stir in oats and raisins. Add oil, egg, milk, carrots, and banana and stir until just blended.
Fill each muffin cup with 1/4 cup batter. Bake until a toothpick inserted in center of a muffin comes out clean, 18-25 minutes. Serve muffins warm or at room temperature.