Prepare grill to medium-high heat.
To create glaze:
combine brown sugar, mustard, rice vinegar and soy sauce in medium bowl then whisk to blend.
Brush 1 side of salmon fillets generously with half of glaze. Place salmon steaks, glazed side down, onto barbecue. Grill until glaze is slightly charred, about 4 minutes. Brush top of salmon steaks with remaining glaze. Turn salmon over and grill until second side is slightly charred and salmon is just opaque in center, about 5 minutes longer. Transfer salmon to plates.