In heavy 12-inch skillet over moderately high heat, heat ¼ cup oil. Sear the bison ribs, turning with tongs, until well-browned on all sides, about 8 minutes total. Transfer ribs, bone side up and in 1 layer, to a 3- to 4-inch-deep roasting pan and set aside. Do not clean skillet.
Add onions, carrots, celery and mushrooms to skillet. Over moderately high heat, sauté until onions start to soften, about 5 minutes.
Transfer vegetables to wide, 6-quart sauce pot. Deglaze the cooking pot with the red wine, making sure to scrape up any brown bits from bottom and sides of skillet. Add stock and bring to boil. Pour stock mixture over ribs and cover with foil. Transfer to oven and braise until meat is tender and falling off bone, about 7 hours.
Chef’s Note: Bison short ribs take much longer than beef ribs—the ribs will need a long, slow braise to tenderize. This can be braised overnight in a Crock-Pot.
To make sauce:
Strain cooking liquid into medium saucepan. Skim fat. Reserve cooked carrots and celery for sauce. Bring to a boil and continue cooking until reduced to about 1½ cups, about 25 minutes. For a thicker sauce combine 1 tablespoon cornstarch and 1 tablespoon water to make a slurry and add to sauce. To serve, add back carrots and celery, and spoon braising liquid over sauce.
Serve over your favorite mashed potatoes. Chef Paul serves over Blue Cheese Mashed Potatoes made with Kenny’s Blue Cheese.
Chef’s Note: If you can easily remove the bone from the rib meat, it is an indication that the rib is perfectly cooked.