Preheat oven to 350°. Fold 4 pieces of parchment paper (12 by 14 in. each) in half to form 7- by 12-in. rectangles and cut them into half-heart shapes as large as the paper allows. Unfold into hearts. Place a fish fillet to one side of center of each heart and sprinkle with 1/4 of the salt. Spread each fillet with 1/4 of the ginger. Drizzle with 1/4 of the sesame oil and top with 1/4 of the green onions. Fold papers over fillets and crimp edges to close (see "How to Make a Parchment Packet," below).
Put packets on a baking sheet and bake 15 minutes, or until the fish is opaque and flakes easily in the center; if necessary, cook 5 minutes more. Serve hot.
How to Make a Parchment Packet: The key to cooking en papillote starts with the shape of the paper. Fold a piece of parchment paper, about 2 1/2 times the size of what you'll be cooking, in half and cut it into a half-heart shape. Unfold, fill one half with the ingredients, and fold the other half over to enclose. Starting at the top of the heart in the center of the dip, fold about 1/4 in. of the edge toward the center and start rolling this "hem" around the edge, crimping the roll as you seal it. When the roll reaches the bottom tip of the heart, twist to seal. When using aluminum foil, simply fold foil over contents and crimp edges to seal.
Note: Nutritional analysis is per serving.