Peel and cut the carrots into chunks, then add them to a medium saucepan. Cover with water by at least an inch, and cook until soft (15-20 minutes). Drain water from the carrots and return the pot to the stove on low heat to dry the excess moisture, being careful not to burn them.
Preheat the oven to 350℉ (180℃).
Place the carrots in a large bowl while still hot, then add the brown sugar, baking powder, and vanilla extract and mash into a puree.
Add the flour, salt, cinnamon, and nutmeg, and mix thoroughly.
Beat the eggs, add them to the batter with the milk, and stir well with a wooden or stainless steel spoon.
Add the melted butter, and continue mixing until fully combined.
Spray a 4”x8”×8” casserole or oven-safe dish with non-stick cooking spray, and, optionally, lightly coat with flour. Pour the batter into the dish about ¾ full.
Bake at 350℉ (180℃) for 30-40 minutes or until fluffed and set.