Preheat the oven to 350 degrees F and line a muffin tin with baking cups.
In a large bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, nutmeg, and ground cloves. Set aside.
In a separate bowl, whisk together melted butter, brown sugar, egg/flax egg, sour cream, and vanilla extract. Gently stir in the grated carrots.
Add the dry ingredients to the wet and gently fold until just incorporated. Scoop the mixture into the prepared baking cups, filling them about 3/4 full. Bake for 20 minutes or until a toothpick comes out clean.