On a plate or in a shallow bowl, combine the flour, allspice and a generous pinch of salt and grinding of pepper. Pat the chicken dry. Trim any excess fat. Leave the skin on or remove it, as you prefer. Dredge chicken in the flour mixture, shaking off any excess.
Heat 1 tablespoon of oil in a large Dutch oven or sauté pan over medium-high heat. Working in two batches to avoid overcrowding the pan, sear the chicken 2-3 minutes per side, or until golden. Transfer to a plate. Repeat with remaining oil and chicken.
Add onion, garlic and a generous pinch of salt to the pan. Sauté 3 minutes, or until tender. Add stock, lemon juice and honey, scraping the bottom of the pan to loosen any browned bits.
Return the chicken, along with any juices that have collected on the plate, to the pan. Cover, reduce heat, and simmer for 35 minutes, or until chicken is done. (Registers 165°F on an instant-read thermometer inserted into the thickest part of the thigh.)
Transfer chicken to a plate, and tent it with foil to keep warm. Increase the heat under the pan to medium high, and bring the braising liquid to a boil. Cook 3-5 minutes, or until the braising liquid is reduced by half and a silky, gravy-like consistency. Season to taste with salt and pepper.
Serve the chicken drizzled with gravy and, if desired, sprinkle with parsley.