01 - Preheat oven to 400°F.
02 - Slice the top off the garlic bulb, drizzle with 1 tbsp olive oil, wrap in foil, and place on a baking sheet with cauliflower florets. Drizzle remaining olive oil over cauliflower and toss to coat.
03 - Roast cauliflower and garlic for 30 minutes, stirring cauliflower halfway through, until golden and tender.
04 - In a large pot, melt butter over medium heat. Add onion, carrots, and celery. Sauté for 5–6 minutes until softened.
05 - Squeeze roasted garlic cloves from skins and add to the pot along with the roasted cauliflower.
06 - Pour in vegetable broth and bring to a simmer. Cook 10 minutes for flavors to meld.
07 - Remove from heat. Use an immersion blender to puree soup until smooth (or carefully transfer to a blender in batches).
08 - Stir in Asiago cheese and milk. Return to low heat, stirring until cheese melts and soup is creamy. Season with salt, pepper, smoked paprika, and nutmeg.
09 - Serve hot, garnished with parsley or chives and extra Asiago cheese if desired.