Add the bacon to a 6-quart or larger round Dutch oven set over medium-high heat and cook until fat is rendered and bacon is crispy, about 6 minutes. Remove bacon with a slotted spoon and set aside to drain on paper towels. Discard (or save for later use) all but 1 tablespoon bacon fat from pot.
Season the chicken with the allspice, 1 teaspoon salt, and 1/2 teaspoon pepper. Add chicken pieces, skin side down, to the pan (in batches if necessary), and cook until nicely browned, 3 to 4 minutes per side. Set aside.
Add onion, chopped fennel, apples, and fennel seeds to the pan and cook, stirring frequently, for 5 minutes, then return bacon to pan. Increase heat to high and add half of the cabbage, the remaining 1 teaspoon salt, and 1/2 teaspoon pepper and cook, stirring, until cabbage is slightly softened, about 5 minutes. Add remaining cabbage to pan and cook for 5 minutes longer. Stir in applejack and once evaporated, return chicken to pan, nestling it in the cabbage. Add apple cider as needed, to cover chicken, and bring to a boil. Reduce heat to low, cover, and simmer until the chicken is very tender, 50 minutes to 1 hour.
Serve in shallow bowls with fennel fronds, grilled apples, and apple chips, if desired.