01 - Preheat oven to 400°F for roasting vegetables and garlic.
02 - Slice the top off the garlic bulb to expose cloves, drizzle with 1 tablespoon olive oil, wrap completely in aluminum foil.
03 - Place cauliflower florets on a large baking sheet, drizzle with remaining 1 tablespoon olive oil, toss thoroughly to coat evenly.
04 - Place foil-wrapped garlic on baking sheet with cauliflower. Roast for 30 minutes, stirring cauliflower halfway through, until cauliflower is golden and tender.
05 - While vegetables roast, melt butter in a large pot over medium heat. Add chopped onion, sliced carrots, and celery. Sauté for 5-6 minutes until softened and fragrant.
06 - Remove roasted garlic from foil, squeeze cloves from skins into the pot. Add roasted cauliflower to the pot.
07 - Pour vegetable broth into the pot. Bring to a gentle simmer, then cook for 10 minutes to allow flavors to meld together.
08 - Remove pot from heat. Use immersion blender to puree soup until completely smooth and creamy, or carefully transfer to countertop blender in batches.
09 - Stir in grated Asiago cheese and milk. Return to low heat, stirring constantly until cheese melts completely and soup reaches desired consistency.
10 - Season soup with salt, black pepper, smoked paprika, and nutmeg. Serve hot, garnished with chopped parsley or chives and additional grated Asiago cheese.