Preheat the oven to 350°F (175°C) and line a muffin tin with paper liners.
In a large bowl, whisk together the flour, baking powder, baking soda, cinnamon, nutmeg, and salt.
In another bowl, beat the eggs, then add the brown sugar, oil, and vanilla extract, mixing well.
Stir in the grated carrots until evenly combined.
Gradually add the dry ingredients to the wet mixture, stirring gently until just combined.
If desired, fold in the chopped walnuts.
Divide the batter evenly among the muffin cups, filling each about two-thirds full.
Bake in the preheated oven for 20-25 minutes or until a toothpick comes out clean.
Allow the muffins to cool in the pan for 5 minutes before transferring to a wire rack.
Enjoy warm or at room temperature!