Prepare the plank by soaking it in water for 45 minutes.
Preheat your oven to 350 degrees, placing the plank in the oven while it preheats. (If you're grilling, you want medium, indirect heat)
When the oven is preheated, remove the hot plank carefully from the oven.
Rinse salmon and pat dry. Arrange skin-side down on plank.
In a small bowl, combine brown sugar, oil, salt and peppers. Spread over salmon.
Place plank on the center rack of the oven. (You may want to line the bottom rack with foil for easy cleanup. Cook fish for about 14-16 minutes. The cooked fish will flake easily. Thinner filets may cook more quickly. A very thick filet may take up to 20 minutes to cook through. (See notes for grilling.)
Serve with a side of lemon wedges. (The fish can be served right on the plank if so desired.)
If you're grilling the salmon, cook for 15-20 minutes with the lid on. Keep in mind that smaller/thinner filets will cook faster.