Bring a bit of water to boil in a soup pot and simmer half the celery and the grated carrot for 3 minutes, then remove and place in some ice water. Reserve the water you simmered the vegetables in to use as part of the broth later.
Heat the butter over medium heat and saute the onion, the rest of the celery and the garlic a few minutes, stirring, then add the broken up cauliflower and cook another few minutes, stirring,
Add 4 cups broth and simmer until the vegetables are soft. Puree with an immersion blender, then add the beer and dry mustard. Bring to a simmer and cook 5 minutes to blend the flavors. Remove from the heat and stir in the grated cheese and then the half and half, if using. Taste and add salt and pepper if needed.