Preheat oven to 400 degrees. Heat 2 teaspoons oil in a heavy skillet over medium-high heat. Sprinkle pork with salt and pepper. Add pork to the skillet and saute until brown, about 3 minutes per side. Remove from heat and transfer the pork to a square baking dish. Add the chicken stock and madeira to the skillet. Place over medium-high heat. Boil until reduced by half, scraping up browned bits, about 6 minutes. Pour over the pork.
Clean and slice the mushrooms. Heat 2 teaspoons butter in the pork skillet. Add mushrooms to the skillet and saute until softened and brown.
Bake pork until tender, about 25 minutes.
Transfer pork chops to serving plates. Place sauce over heat. Add mushrooms and a splash of cream into the sauce and bring to a boil. Stir the fines herbes into the sauce just before serving, reserving some to sprinkle over the pork chops. Spoon sauce over the pork chops. Sprinkle with more fines herbs.
Recipe courtesy of Sara Moulton