Preheat your oven to 350°F (175°C).
In a medium bowl, whisk together oats, oat flour, baking powder, cinnamon, nutmeg, and salt.
In a separate bowl, whisk the eggs, coconut oil, maple syrup, cane sugar, and vanilla until smooth.
Pour the wet mixture into the dry ingredients. Add grated carrots and stir until just combined.
Spread the mixture into a prepared 8x8-inch baking dish.
Bake for 25–30 minutes, or until a toothpick inserted in the center comes out clean.
Let the bars cool in the pan for 5 minutes, then transfer to a wire rack to cool completely before slicing.
To Make the Frosting:
Warm cream cheese in the microwave for about 30 seconds.
Whisk in maple syrup, milk, and vanilla until smooth. Add more milk if needed to thin.
Drizzle frosting over cooled bars and slice into 16 pieces.