Preheat & roast garlic — Preheat oven to 400°F (200°C). Place the two whole unpeeled garlic cloves on a small sheet of foil or a baking tray, drizzle with a little olive oil, and roast 18–22 minutes until soft and caramelized. Set aside.
Render pancetta — In a large Dutch oven or heavy pot, heat 2 tablespoons olive oil over medium heat. Add diced pancetta and sauté until fat renders and pieces are golden-crisp, about 5–8 minutes. (For vegetarian: skip pancetta and use an extra tablespoon olive oil + 1 tsp smoked paprika.)
Build the soffritto — Add diced onion, carrots and celery to the pancetta. Reduce heat to medium-low and sweat the vegetables, stirring occasionally, until softened and translucent, about 8–10 minutes.
Add aromatics — Stir in the minced garlic (reserve roasted garlic) and grated ginger; cook 1–2 minutes until fragrant. Mix in the tomato paste and cook 1–2 minutes, stirring to caramelize the paste slightly.
Deglaze — Pour in the white wine and scrape up any browned bits from the pot bottom. Let the wine reduce for 2–3 minutes until mostly evaporated.
Simmer the soup — Add chicken stock, Parmesan rind, bay leaf, and rosemary. Bring to a gentle simmer, then reduce heat to low and simmer uncovered for 25–30 minutes. Add shredded chicken during the last 10 minutes to heat through (if using).
Finish with the “penicillin” touch — Remove and discard the Parmesan rind and rosemary sprig. Mash the roasted garlic into a paste and add to the pot. In a small bowl, whisk together honey and lemon juice; stir into the soup gradually and taste. Adjust honey, lemon, and grated ginger to balance sweetness and brightness. Season with salt and pepper.
Optional texture control — For a silkier mouthfeel, remove 2–3 cups of the soup and puree until smooth, then stir back in. Or pulse briefly with an immersion blender, leaving some texture.
Plate & garnish — Ladle into warmed bowls. Finish each bowl with a drizzle of extra-virgin olive oil, lemon zest, chopped parsley, and shaved Parmesan or toasted breadcrumbs if desired. Serve with crusty bread or crostini.