Season short ribs with salt, pepper, and seasoning mix. Heat a large roasting pan with lid over medium high heat and add oil. Sear ribs in hot oil on all sides until well browned.
Remove from roasting pan and set aside. Add peppers, onions, celery and garlic and cook until well browned. Deglaze roasting pan with red wine, then add barbeque sauce and stock and bring to a boil. Return ribs to roasting pan and cover tightly with foil. Place in preheated oven and braise for 2 1/2 hours, or until meat is tender when pierced with a fork.
Remove ribs from sauce and keep warm. Skim fat from the top of sauce and season with salt and pepper. Pour sauce over short ribs and serve with horseradish mashed potatoes and sweet corn salad with basil vinaigrette.