Cut cauliflower head in to small pieces. Toss with 1 tablespoon olive oil and roast until tender, 20-25 minutes.
In a large pot, heat remaining olive oil over medium heat. Mince garlic, add to pot, and cook for one minute. Stir in roasted cauliflower, thyme, salt, pepper, and 3 cups veggie broth. Bring to a boil, reduce to a simmer, and let cook for 8-10 minutes.
Remove from heat and using a blender or an immersion blender, puree soup. Return to a medium heat and let cook for 3-4 more minutes, tasting and adding more salt/pepper as needed.
Remove from heat and stir in cheddar cheese until melted. Serve with a sprinkle of parmesan cheese.