In a small bowl combine the apple juice or cider and vinegar. In a medium saucepan combine the fennel wedges, 1/2 cup of the apple juice mixture, the bouillon granules, and garlic. Bring to boiling; reduce heat. Simmer, covered, for 14 to 16 minutes or until the fennel is tender.
Remove upper stalks from fennel, including feathery leaves; reserve leaves and discard stalks. Discard any wilted outer layers on fennel bulbs; cut off a thin slice from each base. Wash fennel and pat dry. Quarter each fennel bulb lengthwise. Chop enough of the reserved fennel leaves to make 2 teaspoons; set aside along with a few sprigs of the feathery leaves.
Meanwhile, pour oil into a large skillet or wok. Preheat over medium-high heat. Add the cabbage; stir-fry for 3 to 5 minutes or until cabbage is crisp-tender. Combine the remaining apple juice mixture and the brown sugar; stir into cabbage along with the fennel seed. Cook and stir about 1 minute more or until heated through.
Transfer the cabbage to a serving platter. Remove the fennel wedges from the liquid with a slotted spoon. Place on top of cabbage. Garnish with the reserved chopped fennel leaves and the reserved sprigs. Makes 4 to 6 servings.