Unlike traditional coq au vin, this dish is made with white wine, which makes it a little lighter than the red wine version.
Heat 2 tablespoons olive oil in a large Dutch oven over moderately high heat. Add ham and saute until browned all over. Remove ham, leaving as much of the oil in the pan as possible, and set aside.
Liberally season chicken with salt and pepper, then dredge in flour. Add the remaining oil to the Dutch oven and raise heat to high. Working in batches, sear pieces of chicken thoroughly on all sides until well browned. Set aside.
Adjust heat to a moderate flame. Add onion, garlic, shallots, and mushrooms, then saute 3 minutes, stirring constantly, until tender and fragrant. Add wine, stock or broth, carrots, celery, and thyme, then let mixture come to a boil. Add the reserved chicken in two layers, then top with ham. The liquid should barely cover the top layer of chicken. Cover pot and adjust heat to a low simmer. Cook 45 to 50 minutes until chicken is very tender and sauce has thickened from the flour. Correct seasoning with salt and pepper. Garnish with thyme sprigs and serve with rice, noodles, or roasted potatoes.