On rimmed baking sheet, spread cauliflower out in a single layer. Drizzle with olive oil and sprinkle with salt and pepper. Toss to coat.
Roast cauliflower on center rack of oven until tender at the edges, about 10 – 15 minutes. Set aside.
Add butter to a 6 quart dutch oven or similar size pot. When melted, add garlic and thyme; cook while continuing to stir until fragrant, about 1 minute.
Stir in broth, cream and cayenne. Bring to a simmer over medium heat.
Add in cauliflower, stir and bring mixture to a boil. Reduce heat and simmer for 10 minutes.
Using an immersion blender (or transfer to upright blender in batches), blend until smooth or until desired consistency is reached. If soup is too thick, add additional cream or milk by the tablespoon until soup is at desired consistency.
Ladle into bowls and serve warm. Garnished with thyme leaves and shredded cheddar cheese (optional)