Melt unsalted butter (2 tablespoons) in a large heavy bottom pot over medium heat.
Add chopped white onion (1/2 cup), and cook until translucent, about 10 minutes.
Add minced garlic (4 cloves) and stir for 1-2 minutes, or until fragrant.
Add xanthan gum (1 teaspoon), and stir into the veggies until it dissolves.
Add the vegetable broth (3 1/2 cup), and heavy cream (1 cup). Bring the soup to an aggressive simmer. Reduce uncovered for 10 minutes. You'll know it's done once the soup coats the back of a spoon.
Add broccoli florets (4 cups) and continue to cook until the broccoli is tender about 20 minutes.
Working in batches, add the soup to a high-speed blender* and blend until smooth. Alternatively, you can use an immersion blender.
Return soup to the pot, and make sure the heat is off.
Add shredded cheddar cheese (3 cups), 1 cup at a time. Stir in until melted.
Taste the seasoning, and adjust as needed. I usually add 1/2 additional teaspoon of salt here.
Ladle into bowls, and enjoy!