Preheat oven to 350 degrees F.
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, about 10 minutes. Deglaze roasting pan with red Zinfandel, then add BBQ 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.