Position a rack in the center of the oven and heat the oven to 350°F.
Grease 12 regular-sized muffin cups or line with paper cups.
In a medium bowl, whisk both flours, quick oats, cinnamon, baking soda, baking powder, nutmeg, and salt.
In a large bowl, whisk the eggs, carrot purée, sugar, oil, and honey until well combined.
Add the dry ingredients to the wet and stir with a large spoon just until evenly incorporated.
Spoon the batter into the prepared muffin pan 2/3 full.
Bake until the muffins are golden and a toothpick inserted in a muffin comes out clean, about 16 to 18 minutes.
Cool in the pan for 5 minutes and then transfer the muffins to a wire rack to cool.
Bake these in a mini muffin tin for mini carrot muffins. Bake muffins for 13 to 15 minutes or until toothpick inserted in middle of muffin comes out clean.
Store carrot muffins in an airtight container at room temperature for up to 3 days. They can be refrigerated for up to a week and frozen for up to three months in a food storage freezer bag. Thaw the muffins overnight in the refrigerator. Warm them in a low oven for a few minutes for a freshly baked taste.