In a large, heavy skillet, heat the oil or bacon drippings over medium high heat until hot but not smoking.
Season the chicken with salt and pepper. Brown the chicken on both sides in the hot skillet, about one minute per side, but do not cook all the way through. Remove to a casserole dish.
Add the prosciutto to the chicken drippings and cook about 2 minutes until crisp. Remove to casserole dish on top of the chicken.
Chop the artichoke hearts into large pieces and reserve the liquid. Add the mushrooms, artichokes, and garlic to the pan and reduce heat to medium. Saute about 5-7 minutes until the garlic is soft and the liquid has evaporated from the mushrooms. Spoon mixture over the chicken in the casserole dish.
Pour the reserved liquid from the artichokes into the pan, along with the wine or broth. Add the flour, wisking briskly to remove any lumps. Once mixture has thickened, pour over chicken and mushroom mixture.