Choose a heavy Dutch oven or skillet with a tight-fitting cover, large enough to fit the chicken in no more than two layers plus the vegetables. In this pan, heat 1 tablespoon of the oil, add the ham and saute until browned all over. Remove and reserve the ham, leaving as much of the oil in the pan as you can.

Liberally season the pieces of chicken with salt and pepper and dredge them in the flour. Add the remaining oil to the pan. When the oil is hot, sear the pieces of chicken thoroughly on all sides until well browned. Take care not to scorch the flour coating, but do let it get brown. Do this in batches. Reserve the chicken with the ham.

Return pan to the burner and set to medium. Add the onion, garlic, shallots, and mushrooms, and saute for 3 minutes, stirring constantly, until tender and fragrant. Add the wine, chicken broth, carrots, celery, and thyme, and let the pan come to a boil. Add the reserved chicken and ham. Cover the pot and bring to a simmer. Cook for 45 to 50 minutes, until the chicken is very tender and the sauce has thickened from the flour. Taste and correct seasoning with salt and pepper.

Arrange chicken pieces and vegetables on a warmed platter, and cover with the sauce. Serve with rice, noodles or roasted potatoes.