Into a medium saucepan over medium-high heat, add the carrots, onion, celery, garlic, cayenne pepper sauce, salt, black pepper, vegan chicken broth, and beer. Bring to a boil then reduce to a simmer for about 15 minutes, or until the vegetables are tender. Add the Dijon mustard, Worcestershire sauce, and yellow mustard; stir to combine and set aside.

Into a separate large pot over medium heat, add the butter. When the butter is melted, add the flour and stir until thickened. Whisk in the milk and continue stirring to incorporate. Add the cheese and stir until melted.

Add in vegetable mixture, reduce to medium-low heat, and simmer for 10 minutes, until heated through. (For a creamy texture, transfer soup to a high-speed blender or food processor and puree to desired consistency. Alternatively, use an immersion blender to puree the soup right in the pot.)Adjust seasoning to taste and serve hot.