Preheat the oven to 400°F.
Add the tomatoes, onion, garlic bulb, olive oil, thyme, salt, and pepper to a baking dish.
Roast for 30 minutes until the vegetables are softened and lightly caramelized.
Transfer the roasted vegetables to a large pot. Squeeze the roasted garlic cloves from the bulb into the pot.
Add the broth, heavy cream, Parmesan cheese, sugar, and bay leaves.
Bring the mixture to a boil, then reduce heat and simmer for 5–10 minutes.
Remove the bay leaves.
Use an immersion blender to blend until smooth. Alternatively, carefully transfer the soup to a blender and blend until creamy.
Taste and adjust salt and pepper as needed.
Serve warm with additional Parmesan, fresh thyme, or your favorite grilled cheese sandwich.