Season the chicken pieces. Heat oil in a large casserole over high heat. Brown the chicken all over in batches. Remove and set aside.
In the same pan, fry the lardons until crispy. Remove. Add the pearl onions and cook until golden. Remove. Add the mushrooms and cook until browned. Remove.
Add the garlic to the pan and cook for 1 minute. Stir in the tomato paste, then sprinkle in the flour and cook for 1 minute.
Pour in the wine, scraping up the browned bits. Add the carrots and bouquet garni. Return the chicken to the pan.
Bring to a boil, then reduce to a gentle simmer. Cover and cook for 1 hour.
Return the lardons, pearl onions and mushrooms to the pan. Simmer uncovered for 20 minutes until the sauce is thickened and the chicken is very tender.
Stir in the butter for richness. Adjust seasoning. Garnish with parsley and serve with mashed potato or crusty bread.