Preheat oven to 350 degrees F. Spray 9x13" baking pan with cooking spray.
In a large bowl with electric mixer, beat together the butter and sugar until well combined about 1 minute.
Add the egg and vanilla and beat another minute.
Add the banana and beat another minute.
Add flour, baking powder, baking soda, salt, cinnamon, and nutmeg and beat until just combined.
Fold in zucchini.
Pour batter into prepared baking dish.
Bake for 28-32 minutes, until middle is set and toothpick comes out clean.
Let cool completely
Meanwhile, make the brown butter.
Add butter to a small pot over medium-low heat.
Melt the butter and let it cook until little brown specks form and you smell a nutty aroma. Remove from heat immediately.
Let cool for about 20 minutes.
In a large bowl with electric mixer, beat together brown butter and cream cheese.
Add vanilla, salt, and powdered sugar and beat until well combined.
Spread over cooled bars.
Cut into slices and enjoy!