Roast garlic and cauliflower: Preheat oven to 400°F (200°C). Cut the top off the head of garlic, exposing the cloves. Drizzle with olive oil, wrap in foil, and place on a baking sheet. Toss the cauliflower florets with olive oil, salt, and pepper. Spread them on the same baking sheet around the garlic (you can use a separate baking sheet if needed). Roast for 30-40 minutes, or until the cauliflower is tender and slightly browned and the garlic cloves are soft and easily squeezed out of their peels.

Sauté onion: While the cauliflower and garlic are roasting, heat 2 tablespoons of olive oil in a large pot or Dutch oven over medium heat. Add the chopped onion and cook for 5-7 minutes, until softened.

Add broth and cauliflower: Add the vegetable broth to the pot. Once the roasted cauliflower is cool enough to handle, add it to the pot. (Reserve a few florets for garnish if desired.)

Simmer and blend: Bring the mixture to a simmer and cook for 10-15 minutes, allowing the flavors to meld. Carefully squeeze the roasted garlic cloves out of their peels and add them to the pot. Use an immersion blender to blend the soup until smooth and creamy. Alternatively, you can carefully transfer the soup to a regular blender in batches.

Add cheese and cream: Reduce heat to low. Stir in the shredded cheddar cheese until melted and smooth. If using heavy cream, stir it in now as well. Season with thyme, salt, and pepper to taste.

Serve: Serve the Roasted Garlic Cheddar Cauliflower Soup hot, garnished with extra shredded cheddar cheese, fresh parsley, and croutons, if desired.