Preheat your gas grill to medium heat, around 350°F. If using oven, preheat oven to 375°F.
Place each salmon fillet on each cedar plank. Brush salmon with olive oil. Season generously with salt and pepper. Sprinkle dill weed and brown sugar evenly on the fillets.
Place the cedar plank on the grill and cover. Grill for about 12-15 minutes and check for doneness. If using oven, bake at 375°F for 15 minutes. Switch to broil and broil on high for an additional 5 minutes until the surface of the fish is slightly browned.
Using tongs and oven mitts, remove the cedar plank salmon and transfer to a flat surface to rest.