Preheat oven to 400°F and line muffin tin
In a medium bowl, whisk together flour, baking powder, baking soda, salt, nutmeg, and cinnamon until evenly combined
In a separate bowl, whisk banana and brown butter until combined, then mix in sugars until smooth
Add egg, greek yogurt, and vanilla to wet ingredients and mix until smooth
Gently fold dry ingredients into wet ingredients until mostly combined with a few streaks of flour remaining
Add finely shredded carrots and fold until incorporated, avoiding overmixing
Pour batter into prepared muffin pan and smooth the top
Bake for 5 minutes, then reduce temperature to 350°F and bake for 30-35 minutes until toothpick comes out clean or with just a few moist crumbs
Cool muffins in pan for 15 minutes, then transfer to rack to cool completely
For frosting: beat softened cream cheese and butter until smooth and fluffy
Add powdered sugar and mix until fully incorporated
Mix in maple syrup, cinnamon, and vanilla bean paste and beat until smooth and creamy
Adjust consistency with more maple syrup or powdered sugar as needed
Spread frosting over cooled muffins
