Preheat oven to 350°F (175°C). Line muffin tin with papers or grease well.
Grate carrots using a box grater or food processor.
In a large bowl, whisk together flour, baking powder, cinnamon, baking soda, salt, ginger, and nutmeg.
In another bowl, mix eggs, oil, honey or maple syrup, applesauce, and vanilla extract.
Add wet ingredients to dry ingredients and stir just until combined. Batter will be thick.
Fold in grated carrots and optional mix-ins. Do not overmix.
Divide batter into muffin cups, filling each about 3/4 full.
Bake 18-22 minutes, or until a toothpick inserted comes out clean.
Cool in pan for 5 minutes, then transfer to wire rack. Let cool completely before storing or frosting (if using).