Start by melting butter over medium-low heat in a dutch oven or pot. Sauté the onion for 3-5 minutes.
Add garlic and continue sauteing for an additional 3 minutes.
Pour in chicken broth, heavy whipping cream, carrot, dijon mustard, salt, and pepper. Stir and bring mixture to a simmer for 15 minutes.
Add broccoli florets and cook for 12-15 minutes until they reach your desired level of tenderness.
Add chicken and stir until well distributed, then gradually stir in cheddar cheese until completely melted. If you would like to thicken the soup, sprinkle xanthan gum evenly over surface of soup and whisk until soup begins to thicken.
After removing from heat, season with salt and pepper to taste before serving.