If you use the larger sea scallops, halve or quarter them.
Rinse scallops under running cold water. Drain and toss with lemon juice.
In medium heavy skillet, heat butter and oil until sizzling. Add scallops, garlic and ginger; cook briefly for 1 to 2 minutes, turning scallops over once with tongs.
Have ready and buttered 4 individual coquille dishes or a medium gratin dish. Place scallops, along with butter-ginger juices into dish; spread evenly.
Sprinkle with bread crumbs, chives and, lastly, the Parmesan.
Place dish 5" below broiler element and broil just to melt cheese and lightly toast crumbs, 3 to 5 minutes. Serve at once.