Combine the cola, onion, brown sugar, garlic, ketchup, ginger, mustard, Worcestershire, and salt in a large bowl. Add the chicken and toss to coat. Cover and refrigerate for at least 1 hour.
Remove the chicken from the marinade; set the marinade aside. Pat the chicken dry. In a deep skillet set over medium-high heat, heat 1 inch of peanut oil. Working in batches, fry the chicken, turning occasionally, until the skin begins to crisp and brown, about 7 minutes. Transfer the chicken to paper towels to drain. Discard the oil.
Put the reserved marinade and chicken broth into the skillet and bring to a boil over high heat. Reduce the heat to low and add the chicken. Simmer for 15 minutes, turning once. Transfer the chicken to a serving platter.
Boil the sauce, stirring occasionally, for 5 minutes or until thickened slightly. Pour the sauce over the chicken.