Preheat oven to 425F.
Rough chop the onion and put in large roasting pan. Separate garlic into cloves, remove skins, and add to pan. Cut cauliflower into florets and add to pan. Drizzle olive oil over all and toss with rubber spatula to evenly coat.
Bake for 30 minutes, stirring halfway through.
In large soup pot, melt butter plus 1 T. olive oil over medium heat. Saute carrots and celery 5 minutes. Add 1 cup of the broth, cover and cook about 10 minutes to soften veggies.
Set aside about 2 cups of the smaller cooked cauliflower florets. Add remaining roasting pan ingredients to the soup pot along with remaining stock. Blend to desired smooth consistency with an immersion blender.
On medium heat, stir in cream and milk. When hot, stir in the shredded cheese a little at a time so it melts. Add salt and pepper to taste. Add reserved cauliflower florets.
Serve hot with crackers.
