Preheat oven to 400°F (200°C). Slice off the top 1/4 inch from the heads of garlic, exposing the cloves. Place them on a small baking sheet or in aluminum foil. Drizzle with 1 tbsp olive oil, season with salt and pepper. Wrap loosely in foil. Roast for 35-40 minutes, or until cloves are very soft and golden brown. Let cool slightly, then squeeze the roasted garlic out of their skins into a small bowl. Mash with a fork and set aside.

While the garlic roasts, heat 2 tbsp olive oil in a large pot or Dutch oven over medium heat. Add the diced onion and cook, stirring occasionally, until softened and translucent, about 5-7 minutes. Add the minced fresh garlic and cook for another 1-2 minutes until fragrant, being careful not to burn it.

If using, pour in the white wine and scrape up any browned bits from the bottom of the pot. Let it simmer until almost completely evaporated, about 2-3 minutes.

Add the mashed roasted garlic, chicken or vegetable broth, fresh thyme sprigs, and bay leaf to the pot. Bring to a gentle simmer, then reduce heat to low, cover, and let it gently cook for 15-20 minutes to allow the flavors to meld.

Remove the thyme sprigs (discard) and bay leaf from the soup. Add the torn bread pieces to the pot. Simmer for another 5 minutes, allowing the bread to soften and begin to thicken the soup. For a smoother soup, use an immersion blender to blend directly in the pot until the desired consistency is reached. Alternatively, carefully transfer portions to a regular blender and blend until smooth, then return to the pot.

Taste the soup and adjust seasoning with salt and freshly ground black pepper as needed. Ladle the hot soup into bowls. Garnish with fresh parsley or chives, a drizzle of extra virgin olive oil, and serve immediately with crusty bread or croutons.