Preheat your oven to 350°F (175°C) and line a muffin tin with paper liners.
In a large bowl, whisk together the flour, sugars, baking soda, baking powder, cinnamon, nutmeg, and salt.
In another bowl, beat the eggs and mix in the oil.
Pour the wet ingredients into the dry ingredients and stir until just combined.
Fold in the grated carrots and walnuts if using.
Distribute the batter evenly into the muffin tin, filling each cup about 2/3 full.
Bake for 20-25 minutes or until a toothpick inserted comes out clean.
Remove from the oven and let cool for 5 minutes in the tin.
Transfer muffins to a wire rack to cool completely.
Enjoy warm or at room temperature!