Add scallions, Scotch bonnet peppers, garlic, broth, ketchup, brown sugar, Worcestershire, ginger, browning sauce, allspice, thyme, bouillon cube (if using), and bay leaves; season with black pepper. Scrape the bottom of the pot and cook over medium-high heat, stirring occasionally, until warmed through and fragrant, about 5 minutes. Add chicken and any accumulated juices and bring to a boil. Cover the pot and reduce heat to medium-low. Cook until liquid is slightly reduced and an instant-read thermometer inserted into the thickest part of chicken registers 160°, about 15 minutes.