Preheat your oven to 400°F (200°C).
Prepare the garlic by cutting off the top of the bulb to expose the cloves. Drizzle with a little olive oil and wrap in aluminum foil.
Place the cauliflower florets on a baking sheet, drizzle with olive oil, and season with salt and pepper. Toss to coat evenly.
Roast the cauliflower and the garlic in the preheated oven for about 25 minutes or until the cauliflower is tender and slightly browned, and the garlic is soft.
In a large pot over medium heat, add a bit of olive oil and sauté the chopped onion until it becomes translucent, about 5 minutes.
Once the cauliflower and garlic are done roasting, add them to the pot with the sautéed onion. Pour in the vegetable broth and bring to a simmer.
After about 10 minutes of simmering, remove the pot from the heat. Blend the mixture using a blender or an immersion blender until smooth.
Return the smooth soup to the pot over low heat, and stir in the heavy cream and shredded cheddar cheese. Mix until the cheese is melted and the soup is creamy.
Season with salt, pepper, and thyme (if using) to taste.
Serve hot, garnished with fresh parsley if desired.