Preheat oven to 350° degrees.
In a large braising pan with a lid or a dutch oven, heat the oil over medium-high heat. Rub the short ribs with half of the spices in the spice packet. When the oil is very hot, add in the short ribs, making sure they're not overlapping, and let them sear for 1-2 minutes or until browned. Flip the short ribs and sear for another 1-2 minutes. Remove pan from heat and place the short ribs on a plate and set aside.
Return the pan to medium heat and add in the onion, celery, carrot, and the other half of the spice pack. Let the vegetables saute for 3-4 minutes, or until they start to soften. Add in the tomato paste and garlic and cook for another minute, stirring occasionally.
Pour the broth into the pan, scraping the bottom to release any stuck on bits, then pour in the Cookin' Sauce pack. Place the short ribs back into the pan and let the mixture come to a heavy simmer. Reduce heat to very low, cover with a lid, put in the oven and cook for 2-2 1/2 hours or until the meat is tender and falling off the bones.
Carefully remove the pan from the oven, remove the lid, and let cool for a bit. Before serving, spoon as much fat as possible from the surface of the sauce. Season to taste with salt and pepper. Serve over or alongside warm mashed potatoes or polenta. Spoon the sauce on top and garnish with chopped parsley.
Slow Cooker version: After searing the short ribs, place them in a slow cooker, along with the sauteed vegetables. Pour the broth and sauce pack in the slow cooker, stir to combine. Cook over high heat for 3-4 hours or on low heat for 7-8 hours.