Mix flour, garlic salt, and pepper, then coat chicken quarters thoroughly. As oven preheats to 350° F, melt 2 Tbs of the butter in a shallow baking dish just large enough to hold the chicken in a single layer. Arrange chicken, skin side down, in butter. Bake, uncovered, 30 minutes.
Meanwhile, melt remaining 4 Tbs butter with honey, lemon juice, soy sauce, and ginger. When chicken has baked 30 minutes, turn it skin side up. Evenly pour on butter mixture. Continue baking, brushing occasionally with sauce, until chicken is tender and richly browned (30 to 40 minutes more).