Mix the Cajun seasoning, oregano, cumin, and paprika in a small bowl to blend, and rub the mixture all over the ribs. Wrap the ribs in heavy-duty foil, encasing them completely, and refrigerate for at least 1 hour and up to 1 day.

Preheat the oven to 350 degrees F. Place the wrapped ribs on a heavy baking sheet and bake in the foil for about an hour, or until the meat is very tend. Unwrap the ribs and let them cool.

Meanwhile make the barbecue sauce: Melt the butter in a large heavy saucepan over medium heat. Add the onions and celery, and sauté for 5 minutes, or until the vegetables are tender. Mix in the beef broth and all the remaining ingredients, and bring to a boil over high heat. Then reduce the heat to medium-low and simmer, uncovered, stirring occasionally, for 1 hour, or until the sauce reduces and thickens slightly.

Coat the ribs with half of the sauce and marinate for at least 1 hour at room temperature or for up to 1 day in the refrigerator. Reserve the remaining barbecue sauce.

Preheat the oven to 350 degrees F. Place the ribs on a foil-lined rimmed baking sheet and roast, uncovered basting often with some of the remaining barbecue sauce, for about 25 minutes, or until the ribs are heated through. Rewarm the remaining sauce and serve it alongside the ribs.