Cut the shiitake mushroom caps in half and place them in a mixing bowl. In a medium saucepan, combine the marinade ingredients and bring to a simmer; simmer for 10 minutes. Remove from the heat and pour the hot liquid over the mushroom caps. Marinate for 20 minutes.
Cut the flank steak across the grain into 1/4-inch strips. Cut the scallion tops into 1-inch pieces.
Remove the mushrooms from the marinade and set the marinade aside. Use a skewer to pierce the flank steak at the end of the strip. Next pierce a piece of mushroom cap, followed by a scallion top. Weave the flank steak strip around the mushroom and scallion and continue skewering mushroom, scallion, and flank steak until the steak strip ends. Lightly season the skewers with salt and pepper.
Preheat a hot grill. Dip each skewer into the leftover marinade and place on the grill over direct heat. Grill for 2 minutes on each side, or until the steak browns. Remove the skewers from the grill and serve.