In a 6 - 8qt soup pot sauté the onions, garlic, and carrots in olive oil until the onions are translucent and garlic is fragrant, about 2-3 minutes.
Stir in the nutmeg, salt, and pepper. Let cook for another minute.
In a small bowl whisk together ¼ flour and 1 cup chicken stock. Pour mixture into the pot. Bring to a boil and let simmer until the liquid thickens a little bit, about 3-5 minutes.
Stir in the rest of the chicken stock, coconut milk, cream cheese, and broccoli. Bring to a boil and then let simmer until the broccoli and carrots are soft and the cream cheese is melted, about 25 minutes. It's okay if there are specks of cream cheese during this step. That will be gone after the soup is blended.
Using a hand blender or regular blender blend the soup until you get the consistency you like. If the soup is too thick then add in more chicken stock until you get the desired consistency.
Stir in the shredded extra sharp cheddar and parmesan. Stir until the cheese melts. Taste for salt and then serve.