Soak the cedar planks. Soak the cedar planks in warm water, weighting with something heavy, like a soup can, so it stays submerged for 30 minutes up to 3 hours before grilling.
Preheat the grill to medium-high. Brush the grill grates of any loose bits to avoid flare-ups.
Prep the salmon. Season the salmon with ½ teaspoon kosher salt and ¼ teaspoon freshly ground black pepper (both sides if using skinned salmon).
Make the barbecue glaze. In a small bowl, whisk 2 tablespoons Japanese barbecue sauce with 1 tablespoon mayonnaise until smooth. Brush each of the salmon filets with the barbecue mixture, evenly coating the tops and sides of the fish. Sprinkle the fish with 1 tablespoon brown sugar, dividing it equally among the filets.
Grill the salmon. Place the soaked cedar planks directly on the hot grill grates, close the lid, and watch until wood begins to smoke, about 5 minutes. Transfer the salmon to the hot planks, cover with the lid, and cook for 5-6 minutes or until the fish is opaque and cooked through. Serve hot or at room temperature. Salmon can be refrigerated for up to 3 days.
Notes
Use tongs or a grilling spatula to transfer the cedar grilling planks to a baking sheet and avoid setting the burned plank bottoms on the counter.