Preheat grill to indirect medium heat. Meanwhile, trim ribs of any excess fat. Lightly salt and pepper ribs to taste; cut to fit 13x9x2-inch aluminum or disposable foil pan. Place ribs, onion, celery and carrot in pan. Pour liquid over ribs. Cover tightly with foil. Place over indirect heat according to manufacturer’s directions. Cover and grill 1 1/2 to 2 hours or until rib meat is very tender.
Melt butter in small saucepan. Add garlic, if desired; cook 30 seconds; do not brown. Stir in barbecue sauce, apple butter and green onion; heat until bubbly. Reduce heat and simmer 5 minutes to blend flavors. Stir in brown sugar, if desired, until dissolved. Set aside.
Heat grill to medium direct heat. Remove ribs from pan; discard liquid and vegetables. Place ribs on grill; brush with reserved barbecue sauce mixture. Cover and grill 15 to 25 minutes or until tender, basting with sauce and turning occasionally.
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