Season the chicken with salt and pepper. In a large skillet with a lid, heat 1 tablespoon olive oil, 1 turn of the pan over medium-high heat. When oil ripples, add chicken and brown about 2 minutes on each side; remove and reserve.
Add remaining olive oil, 2 turns of the pan, and pancetta, and stir 2 minutes. Remove pancetta to a plate and brown mushrooms in drippings, 7-8 minutes; season with salt, pepper and thyme. Add onions, garlic and chilies, and stir 4-5 minutes more. Add tomato paste, stir until fragrant, then add wine, stock, tomatoes and reserved pancetta, and bring to a bubble.
Reduce 15 minutes then add beans and arrange reserved chicken into the sauce among the beans. Cover and cook 5 minutes then remove lid and serve from the pot topped with parsley, tarragon and cheese, with bread alongside.