Preheat oven to 350 degrees. Prepare 12 cup cupcake pan with cooking spray.
Whisk together flour, baking powder, baking soda, cinnamon, nutmeg, and salt. Set aside.
In a large bowl, combine egg, maple syrup, coconut oil, applesauce, milk, and vanilla.
Incorporate flour into wet ingredients until well combined. Fold in grated carrots.
Fill cupcake cups about 1/2 full. Bake for 16-18 minutes. Remove and cool on a wire rack.
For glaze, whisk yogurt well in a small bowl. Add powdered sugar, splash of vanilla, and cinnamon. Whisk until smooth. Add additional sugar or yogurt to reach desired taste/consistency. Drizzle over cooled muffins.