In a large bowl, add carrots, flour, baking powder, cinnamon, and nutmeg. Mix well.
In a separate bowl, beat eggs and mix together with, melted butter, vanilla and brown sugar.
Add the wet ingredients to the carrot mixture and mix until fully incorporated.
Pour batter into a greased 10 x 10 inch cake pan.
Ensure rack is at Bake level. Select Bake. Set temperature to 365°F and set time for 30 minutes. When oven is preheated insert the cake pan into the oven.
When cooking time is completed, carefully remove the cake to a cooling rack.
Let cake cool completely before topping with icing.
Cream Cheese Frosting: Combine all the cream cheese frosting ingredients in a bowl and beat with hand mixer until smooth and creamy.