In a bowl, mix together soy sauce, rice vinegar, water, sesame oil, brown sugar, garlic, and ginger.
In a large bowl or ziplock bag, add the salmon filets and half of the marinade. Let marinade 1-4 hours.
When ready to grill, preheat grill to 450-500F and grease grill grates. I use nonstick spray.
Add marinated filets skin side up (if no skin, it doesn't matter which side), and close grill lid. Discard old marinade.
Let cook 7-8 minutes. Using a fish spatula or delicate spatula, flip fish over. Fish should not be sticking to grill, if it is sticking, let it cook a few more minutes. Once flipped, cook an additional 2-3 minutes or until 130F. Let fish rest 10 minutes.
Heat the remaining fresh marinade in a sauce pan over medium high heat. Once bubbling, add arrowroot slurry. Let bubble another 2 minutes or until sauce has thickened. Turn off heat, it will continue to thicken as it sits.
Brush thickened marinade over top of fish. Top with sesame seeds.