In a stand mixer or large bowl, add the brown sugar, oil, eggs, and vanilla. Mix on medium low until combined.
On low mix in the carrot and mashed banana until just combined.
Add the flour, baking powder, baking soda, salt, cinnamon, ginger, and nutmeg. Fold the dry ingredients in with a spatula until just combined.
In a separate bowl, beat the cream cheese, sugar, and vanilla on medium high until completely combined and smooth.
Spoon a heaping spoonful of batter into the muffin cups. Layer 1 Tablespoon of the cream cheese mixture on top of the batter. Fill the cups to the top with the remaining batter.
Bake for 20-22 minutes or until a toothpick comes out clean.