Heat the oil in a large pan over medium heat. Add the onions and brown sugar. Cook, uncovered, for about 20-30 minutes, until caramelized and sticky.
Add the 1⁄4 cup pomegranate molasses, chicken broth, and pepper to the pan. Cook for 2-3 minutes, until thick. Keep warm.
In a small bowl, mix the barbecue sauce, mustard and 1 tablespoon pomegranate molasses. Set aside.
Sprinkle both sides of the meat with salt and pepper.
On an outdoor oiled grill, or in the oven set to broil, with the meat 6-8 inches from broiler, cook the meat 8 minutes per side. Baste the meat with the prepared sauce. Finish cooking, 2-4 minutes per side.
Remove the meat to a cutting board and let it rest for 10 minutes. Slice the meat into strips and drizzle with the onions.