Prepare chicken: Dust chicken pieces with flour and season with salt and pepper.
Sauté chicken: Heat olive oil and butter in a sauté pan. Add chicken pieces (skin side down optional) and sauté for about 5 minutes on one side until lightly colored, then turn and cook for another 5 minutes.
Remove chicken and cook aromatics: Remove chicken from pan and keep warm. In the same pan, sauté shallots, carrots, and garlic over low heat to avoid burning, for 2-3 minutes.
Deglaze with cognac: Add cognac to the pan to deglaze, raising heat to reduce for about 1-2 minutes without igniting.
Return chicken and add remaining ingredients: Place chicken back in pan on top of vegetables. Add chopped tomato and bouquet garni.
Add wine and simmer: Pour in dry white wine, bring to a light boil, then reduce heat, cover, and simmer for 30 minutes. Optionally remove chicken breasts halfway through and keep warm in a low oven (50-60°C).
Finish chicken: Remove chicken from pan and briefly grill to crisp the skin.
Make sauce: Add cream to the pan and bring to a brisk boil, reducing until sauce coats the back of a spoon.
Season sauce and serve: Adjust seasoning with salt, pepper, and a tablespoon of raw cognac to enhance flavor. Pour sauce over chicken and serve with saffron rice or pasta.