Preheat oven to 350 degrees F.
In a small bowl, whisk together oats, oat flour, baking powder, cinnamon, nutmeg and salt. Set aside.
In a separate bowl, whisk together the egg, milk, coconut oil, maple syrup and vanilla and stir until well-combined.
Pour the wet ingredients in with the dry ingredients, add in the grated carrots, and mix everything until just combined.
Pour the oat mixture into a prepared 8x8-inch baking dish and bake in the oven for 25 to 30 minutes, or until a toothpick inserted in the center comes out clean.
Let the carrot cake bars sit for 5 minutes then remove from pan and let cool completely on a wire rack.
While the bars are cooling, add cream cheese to a small bowl and heat in the microwave for about 30 seconds. Add in the maple syrup, a tablespoon of milk and 1/4 teaspoon of vanilla and whisk together until smooth. Feel free to add more milk a teaspoon at a time until you get your desired consistency.
Slice the bars into 16 pieces and drizzle the cream cheese frosting over top, enjoy!