Put the soy sauce, mirin, sugar, peanut oil, sesame oil, garlic, ginger, green onions, and wasabi, if using, in a blender and process on low for 1 minute, or until the ingredients are well incorporated. Transfer half of the sauce to a shallow dish and add the salmon fillets. Turn to coat well, and refrigerate, turning occasionally, for at least 2 hours and up to overnight. Transfer the remaining sauce to a non-reactive container and refrigerate until ready to cook the salmon. Soak the cedar planks in water for at least 1 hour. (Note: you may have to weight the planks with a heavy object in order to keep them submerged in the water.)
Preheat a grill to medium. Remove the planks from the water and rub the tops each lightly with 1/2 teaspoon vegetable oil. Place 1 salmon fillet on the top of each plank. Place the planks directly on grill and close the cover. (The planks will smoke, this is OK. Keep the lid closed to prevent the smoke from escaping.) Cook until the salmon is just cooked through, about 10 minutes. While the fish is cooking, place the remaining teriyaki sauce in a small saucepan and cook until it has thickened slightly and coats the back of a spoon, 1 to 2 minutes.
Remove the fish from the grill and serve, drizzled with the thickened sauce. Garnish with lime slices and cilantro sprigs.