Heat a 5-quart cast-iron Dutch oven over medium heat. Once hot, add butter along with the onion and celery. Cook for 4-5 minutes until starting to soften. Add in the garlic, cayenne pepper and mustard powder and cook until fragrant, about 30 seconds.

Add the broth and minced broccoli, bring to a boil. Cook until broccoli is softened, about 15 minutes.

Add in half and half and cheddar cheese, stir to combine. Reduce heat to maintain a simmer, add xanthan gum if using. Whisk well.

If you’d like a creamier soup, you can use an immersion blender to blend partially or fully. You can also transfer the soup to a regular blender as well.

Season to taste with salt and pepper, serve immediately.