Preheat the oven to 375F and spray a 12-muffin tin with non-stick spray or line with muffin liners.
Combine the mashed bananas, eggs, brown sugar, vegetable oil, and vanilla extract in a large bowl. Whisk until well combined.
Add the flour, baking powder, and cinnamon and stir until most of the flour has been incorporated.
Add the carrots and fold them into the batter-- make sure to fold just until they’re combined. You don’t want to overmix.
Divide the batter between the muffin tins-- filling each about ¾ of the way full.
Top with chopped nuts or oats, if desired.
Bake for 15-18 minutes or until a toothpick inserted into the center comes out clean.
Remove the muffins to a wire rack to cool.