Preheat oven to 400 degrees.
Core and chop cauliflower (or tear into pieces with your hands). Spread cauliflower and whole garlic cloves in a single layer on baking sheet. Drizzle 1 tablespoon olive oil on top and sprinkle with ¼ teaspoon salt and ¼ teaspoon pepper. Toss to evenly coat.
Roast cauliflower for 20 minutes; turning halfway through. Set aside to cool.
When garlic cloves are cool enough to handle, remove skin and finely chop.
While cauliflower roasts, medium dice onion, carrots and celery.
In a large pot heat 2 tablespoons olive oil over medium heat. Add onion and cook for 2-3 minutes, until they begin to soften.
Add carrots and celery, cook for 5 minutes.
Add chopped garlic, cauliflower, bay leaf, dried thyme and flour. Mix to combine. Cook until flour is well mixed in and begins to disappear, about 2 minutes.
Add vegetable broth, stir well, bring to a simmer. Cook for 10 minutes.
Stir in milk and cheese and continue mixing until cheese is melted, 2-3 minutes.
Discard bay leaf before serving.
Serving Size 1 cup
* Percent Daily Values are based on a 2,000 calorie diet. Your daily value may be higher or lower depending on your calorie needs.