Preheat the oven to 400°F (200°C). Cut the tops off the garlic heads, drizzle with olive oil, wrap in foil, and roast for 30-35 minutes until soft.

In a soup pot, heat a tablespoon of olive oil over medium heat. Add the chopped onion, celery, and carrot. Sauté for about 5-7 minutes until softened.

Once the garlic is roasted, squeeze the cloves out of their skins into the pot with the vegetables. Add the vegetable broth, thyme, salt, and pepper. Bring to a boil.

Reduce heat and let simmer for 10 minutes. Use an immersion blender or transfer to a blender to puree until smooth. If using a blender, be careful with hot liquids.

Stir in the heavy cream if desired, and adjust seasoning to taste. Heat through for another 5 minutes.

Ladle the soup into bowls and garnish with fresh parsley. Serve warm.