Soak the cedar plank in water for at least 2 hours and up to 12.
Preheat the oven to 325 degrees F (165 degrees C), or see Footnote for grilling instructions.
Place the salmon on the plank, skin-side down. In a small bowl, stir together the sesame oil, brown sugar, dill weed and sesame seeds. Stir in just enough water to make it liquid. Season with pepper and soy sauce if desired. Spoon the mixture over the salmon so it is fully coated.
Bake for 30 to 40 minutes in the preheated oven, until the fillet can be flaked with a fork.