On the stove-top, oven medium heat, using a 6-quart dutch oven or large soup pot, sauté the onions and carrots in olive oil until the onions are translucent and the carrots start to soften, about 3-5 minutes.
While the vegetables are cooking, make the slurry for the soup and set it aside. To make the slurry whisk together ¼ cup gluten-free flour and 1 cup chicken stock.
Next, stir the garlic into the onions and carrots, cooking for another 2 minutes or until fragrant.
Stir in the nutmeg, salt, and pepper and let it cook for another minute.
Pour the slurry into the soup pot with vegetables. Bring to a boil and let it 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.
Over medium-high heat, bring the soup to a boil and then turn to medium low heat and bring to a simmer and simmer until the broccoli and carrots are soft, and the cream cheese melts, this takes about 25 minutes. It's okay if there are specks of cream cheese during this step; those will disappear after the soup is blended.
Use an immersion blender to blend the soup until you get the consistency you like. You can also add the soup in batches to a high-speed blender and then pour it into the soup pot to add the cheese. Again, if you like a chunkier soup, use a potato masher to break down the broccoli and carrots.
Turn the heat down to low and then stir in the shredded extra sharp cheddar and parmesan. Continue stirring until the cheese melts slowly.
Taste for salt and then serve.