Preheat oven to 375°F (190°C) and grease a 12-cup muffin tin or line with paper liners.
In a large mixing bowl, whisk together the egg, brown sugar, milk, oil, and vanilla extract until well combined.
Stir the grated carrots into the liquid mixture.
Add the oats, flour, baking powder, baking soda, cinnamon, ginger, and salt to the same bowl.
Fold the dry ingredients into the wet mixture using a spatula until just combined.
Distribute the batter evenly into the 12 muffin cups.
Bake for 18 to 22 minutes or until a toothpick inserted into the center of a muffin comes out clean.
Cool in the tin for 5 minutes before transferring to a wire rack to cool completely.