Warm the butter in the bottom of a 3 or 4-quart pot over medium-high heat. Add the chopped onion and bell pepper, then sauté for 2 minutes until soft. Next, add the garlic and continue cooking for 60 seconds until fragrant.
Pour in broth, beer, and cream. Season with mustard, paprika, salt, and pepper. Bring the liquid to a simmer. Sprinkle xanthan gum evenly over the top of the soup, then stir, and mix well.
Add the cheese, one handful at a time, while stirring briskly in between. Let the cheese melt completely each time before adding more. Otherwise, you risk it clumping up or sticking to the bottom of the pot.
Serve warm with bacon and green onion garnish.
