Combine soy sauce, sake (or wine), mirin, sugar, molasses, Worcestershire and ginger in a small saucepan. Bring to a simmer over medium heat and cook until reduced to 1/4 cup, 2 to 3 minutes. Remove from the heat, pour into a medium bowl, and cool to room temperature, 15 to 20 minutes.

Reserve 1 tablespoon of the sauce in a small bowl. Add scallops and mushrooms to the remaining sauce; stir well to coat. Cover and refrigerate for 30 minutes (but no longer: the scallops will begin to break down if marinated too long).

Preheat grill to medium. Oil the grill rack (see Tip).

Trim scallion whites and reserve for another use. Separate the scallion greens into individual long greens. Wrap one scallion green around the perimeter of each scallop and thread the scallops onto the skewers, piercing through the sides and thereby keeping the scallions in place. Alternate 4 mushroom halves and 3 scallion-wrapped scallops on each skewer. (Reserve any remaining scallion greens for another use.)

Grill the skewers, basting with some of the reserved sauce, for 3 minutes. Turn, baste, and continue grilling just until the scallops are firm and opaque, about 3 minutes more.

Ingredient Notes: Sake is a dry rice wine generally available where wines are sold.

Mirin is a sweet, low-alcohol rice wine essential in Japanese cooking. Look for it in your supermarket with the Asian or gourmet ingredients.

Be sure to buy "dry" sea scallops (scallops that have not been treated with sodium tripolyphosphate, or STP). Scallops that have been treated with STP ("wet" scallops) have been subjected to a chemical bath and are not only mushy and less flavorful, but will not brown properly.

Tip: To oil a grill rack: Oil a folded paper towel, hold it with tongs and rub it over the rack. (Do not use cooking spray on a hot grill.) When grilling delicate foods like tofu and fish, it is helpful to spray the food with cooking spray.

Equipment: 4 bamboo skewers