Over medium-low heat, melt butter in a pot or dutch oven. Add onion and saute for 3-5 minutes.
Add garlic and saute for 3 additional minutes.
Then add heavy whipping cream, chicken broth, carrot, dijon mustard, salt, and pepper, and stir to combine. Bring to a simmer for 15 minutes.
Add broccoli and cook for 12-15 minutes until broccoli has reached your desired tenderness.
Turn heat down to low and slowly stir in cheddar cheese until it is fully melted. If you would like to thicken the soup, sprinkle xanthan gum evenly over surface of soup and whisk until soup begins to thicken.
Remove from heat, season with additional salt and pepper to taste, and serve.