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 and mix until batter is smooth
Add dry ingredients into wet ingredients and gently fold together until mostly combined with a few streaks of flour remaining
Add finely shredded carrots and fold just until everything is incorporated, avoiding overmixing
Pour batter into prepared muffin pan and smooth the top
Bake for about 5 minutes, then reduce temperature to 350°F for 30-35 minutes, or until a toothpick inserted into the center comes out clean or with just a few moist crumbs
Let muffins cool in pan for about 15 minutes, then transfer to a rack to cool completely
For frosting: Add softened cream cheese and butter to a bowl and beat together until smooth and fluffy
Add powdered sugar and mix until fully incorporated
Mix in maple syrup, cinnamon, and vanilla bean paste and continue beating until smooth and creamy
Adjust consistency by adding more maple syrup if too thick or more powdered sugar if too soft
Spread frosting over cooled muffins
