1. Stir together the soy sauce, mirin, ginger, garlic, and brown sugar in a small bowl. Put the salmon in a shallow, nonreactive container, pour the marinade over it, and turn to coat. Cover and refrigerate for 1 to 3 hours.
2. Heat a charcoal or gas grill to medium hot. Away from the heat, lightly spray the grate with vegetable oil spray.
3. Remove the salmon and discard the marinade. Lightly oil the flesh side with olive oil and season with salt and pepper.
4. Grill flesh side down for 3 to 4 minutes. Rotate each fillet 90 degrees for grill marks and cook another 3 to 4 minutes. Turn over and cook skin side down for 2 to 3 minutes for medium.
5. Sprinkle with sesame seeds, if using, and serve.

Note: Mirin is sweetened sake (rice wine), commonly sold in the Asian food section of supermarkets.