Season the chicken all over with salt and pepper and set aside.
To make the barbecue sauce:
In a small saucepan, combine the chicken broth, tomatoes, tomato paste, vinegar, Worcestershire sauce, sugar, molasses if using, and mustard, and whisk to combine. Bring to a simmer over medium heat and cook until fragrant, about 2 minutes. Set aside.
In a 12-inch ovenproof skillet with a lid (cast-iron is great) over medium heat, fry the bacon until the fat renders and it is crisp. Transfer the bacon to a paper towel to drain, leaving the fat in the pan. Discard all but 2 tablespoons fat (or add oil so you have about 2 tablespoons in the pan). Increase the heat to medium-high. Add the chicken, skin-side down, and sear until well browned, about 5 minutes. Turn and brown the other side, about 3 minutes. Transfer the chicken to a plate.
Preheat the oven to 350°F.
Pour out all but 2 tablespoons of the fat from the pan. Reduce the heat to medium and add the onion, bell pepper, celery, and a pinch of salt. Cook, stirring, until the vegetables become tender, about 5 minutes. Add the garlic and red pepper flakes and stir to combine. Stir in the beans and reserved bacon. Set aside ½ cup of the barbecue sauce and add the rest to the bean mixture along with the chicken broth. Bring the mixture to a boil, lower the heat to medium-low, cover the pan, and let simmer, stirring occasionally, for 5 minutes.
Return the chicken to the pan, skin-side up. Cover the pan and transfer to the oven. Cook until the chicken is cooked through, about 30 minutes. Let sit for 5 minutes. Sprinkle with the scallions and parsley and serve, passing the reserved barbecue sauce alongside.