Add the butter, onion, carrot, and celery to a 5-quart pot over medium heat. Cook (uncovered) until the vegetables are softened and starting to caramelize in spots, about 8 minutes, stirring occasionally. Add the garlic and cook 1 minute more, stirring constantly.
Stir in the cauliflower, ale, stock, bay leaf, Dijon mustard, Worcestershire sauce, black pepper, and cayenne pepper. Cover the pot and bring to a boil; turn the heat down slightly so it doesn’t boil over, and cook until the cauliflower is tender, about 15 to 20 minutes, stirring occasionally.
Remove and discard the bay leaf. Carefully puree the soup using an immersion blender or in batches using a regular blender.
Toss the Gouda and tapioca starch together in a bowl.
Turn the heat on low under the soup and stir in the cheese a handful at a time until melted (don’t let it come up to a boil). Taste and add regular salt (not more hickory-smoked sea salt) to taste.