To prepare the brisket, preheat the oven to 350°F. Place the brisket in a large casserole dish or roasting pan; set aside. Combine the chili powder, garlic powder, onion powder, cumin, black pepper, and brown sugar in a small bowl. Rub on both sides of the brisket.
In another small bowl, combine the barbecue sauce and beef broth. Pour over the brisket. Cover the dish or pan with foil and bake for 3 hours. Remove the foil and bake for 1 more hour, or until fork-tender and the liquid has reduced. Allow the brisket to cool then cover and refrigerate it (in the remaining sauce) for 24 hours.
To prepare the quesadillas, preheat the oven to 250°F. Remove the brisket from the fridge and discard any fat that may have accumulated on the surface of the liquid. Place the brisket on a large cutting board and cut the meat, against the grain, into 1/4-inch thick slices. Place half of the brisket slices into a large saucepot with half of its liquid. Heat on low and break up the meat slightly. (Place the other half of the meat and the liquid, if desired, into a zip-top bag or an air-tight container and freeze for later use.)
Lay out 7 flour tortillas. Spread a thin layer of refried beans on one half of each of each tortilla. (Use the whole can.) Divide the warm brisket over the beans. Top with the sautéed onions and cheese and fold up the tortillas.
Pour about 1/3 cup of oil in a large sauté pan or griddle and set the heat to medium-high. Gently place the quesadillas in the hot oil and brown each side. Keep the finished quesadilla warm in the oven and repeat this process until all the quesadillas have been fried. Slice each quesadilla into 4 wedges and serve.