Preheat your oven to 400°F (200°C). Slice about a quarter-inch off the top of each garlic head to expose the tops of the cloves.

Place the garlic heads on a small piece of aluminum foil. Drizzle with 1 tablespoon of the olive oil, ensuring it seeps down into the cloves. Sprinkle with a pinch of salt and pepper.

Wrap the foil loosely around the garlic to create a packet. Roast for 30-35 minutes, or until the cloves are soft, fragrant, and lightly caramelized. Set aside to cool slightly.

While the garlic is roasting, heat the remaining 1 tablespoon of olive oil in a large pot or Dutch oven over medium heat. Add the chopped onion and sauté until softened and translucent, about 5-7 minutes.

Once cool enough to handle, squeeze the roasted garlic cloves out of their skins and directly into the pot with the onions. Mash them gently with a spoon and cook for 1 minute until very fragrant.

Add the diced potatoes, broth, and fresh thyme leaves to the pot. Increase the heat to bring the mixture to a boil.

Once boiling, reduce the heat to low, cover the pot, and let it simmer for 15-20 minutes, or until the potatoes are very tender and can be easily pierced with a fork.

Remove the pot from the heat. Use an immersion blender to purée the soup until it's completely smooth and velvety. Alternatively, carefully transfer the soup in batches to a standard blender and blend until smooth (be sure to vent the lid to allow steam to escape), then return it to the pot.

Place the pot back over low heat. Slowly stir in the heavy cream until fully incorporated. Gently warm the soup through, but do not allow it to boil after adding the cream.

Season generously with salt and black pepper to your liking. Ladle the hot garlic soup into bowls. Garnish with fresh chives, croutons, and a final drizzle of extra virgin olive oil if desired.