Bring a large pot of water to a boil. Add the broccoli, and cook until tender, about 3 minutes. Drain and immediately place in a large bowl filled with water and ice. Drain again.
Preheat your oven to 350° F.
Melt the butter in a saucepan over medium heat. Add the onion and cook for 6 minutes. Add the garlic and thyme and cook for 30 more seconds.
Add the chicken broth, heavy cream, dry mustard, salt, pepper and xanthan gum. Reduce heat to low.
Add 2 cups of the cheddar cheese and cook over low heat until the cheese melts.
Arrange the chicken in the bottom of a casserole dish and top with the broccoli florets.
Pour the sauce over the chicken and broccoli, and top with the remaining ½ cup cheddar cheese and the parmesan cheese.
Bake for 25 to 30 minutes.