How to Make It
In a large skillet, melt the butter in the olive oil. Season the pork medallions with salt and pepper and dust them with flour, tapping off any excess. Add the medallions to the skillet and cook over moderate heat, turning once until browned outside and medium within, about 8 minutes. Transfer the pork to a plate.
Add the mushrooms to the skillet along with the shallots and rosemary and season with salt and pepper. Add 2 tablespoons of the chicken stock and scrape up any browned bits stuck to the bottom of the skillet. Cook over moderate heat, stirring occasionally, until the mushrooms are just beginning to brown, about 6 minutes.
Sprinkle the mushrooms with the 2 tablespoons of flour and cook, stirring, for 1 minute. Pour in the remaining 1 3/4 cups plus 2 tablespoons of stock and bring to a boil, scraping up any browned bits stuck to the skillet. Simmer the gravy over moderate heat, stirring occasionally, until thickened, about 5 minutes.
Return the pork to the skillet along with any accumulated juices and simmer over moderately low heat until warmed through, about 1 minute. Discard the rosemary sprig. Serve right away, with buttered noodles.