Preheat the oven to 375°F (190°C). Line a 12-cup muffin tin with paper liners.
In a large bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, ginger, and nutmeg until well combined.
In a medium bowl, whisk the brown sugar, granulated sugar, eggs, vegetable oil, and vanilla until smooth.
Pour the wet ingredients into the dry ingredients and stir gently until just combined; do not overmix.
Fold in the shredded zucchini and shredded carrots until evenly distributed.
Spoon or scoop the batter evenly into the 12 prepared muffin cups.
Bake for 18 to 20 minutes, or until a toothpick inserted into the center of a muffin comes out clean.
Cool the muffins in the tin for a few minutes, then transfer to a wire rack to cool completely.