Preheat your oven to 400°F (200°C). Slice about 1/4 inch off the top of the entire head of garlic to expose the cloves.

Place the garlic head on a small piece of aluminum foil, drizzle with 1 tbsp olive oil, and wrap it loosely. Roast for 30-35 minutes, until the cloves are soft, fragrant, and lightly golden. Set aside to cool slightly.

While the garlic is roasting, melt the butter in a large pot or Dutch oven over medium heat. Add the chopped onion, carrots, and celery. Sauté for 6-8 minutes, stirring occasionally, until the vegetables have softened.

Once cool enough to handle, squeeze the roasted garlic cloves out of their skins directly into the pot with the vegetables. Mash the cloves gently with the back of your spoon and stir to combine.

Add the cubed potatoes, broth, fresh thyme, salt, and pepper to the pot. Stir everything together and increase the heat to bring the soup 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 easily pierced with a fork.

Remove the pot from the heat. Use an immersion blender to carefully blend the soup directly in the pot until it reaches your desired consistency – either perfectly smooth or with a few small chunks remaining. Alternatively, you can transfer the soup in batches to a standard blender, blend until smooth, and return it to the pot.

Stir in the heavy cream. Return the pot to low heat and gently warm the soup for another 2-3 minutes. Be careful not to let it boil after adding the cream.

Taste the soup and adjust the seasoning with more salt and pepper if needed. Ladle into bowls and serve hot, topped with your favorite garnishes like crumbled bacon, shredded cheese, and fresh chives.