PREHEAT barbecue to medium. Slice each salmon fillet into 6 thin portions, cutting through flesh but not through the skin. Place each fillet on a plank, skin-side down.
STIR together Dijon, oil and salt in a small bowl. Brush over salmon and into the cuts. Sprinkle with brown sugar. Scatter onion overtop.
GRILL, covered, until fillet is barely firm to the touch and white juices appear all over the sides, 20 to 25 min. Turn barbecue off and keep lid closed for 5 min. Fish should now feel firm to the touch and a knife inserted into the thickest part and held for 10 seconds should be warm. If not, close lid and let rest another 5 min. Watch plank carefully; if it catches fire, spray with water and reduce the heat to medium-low.
USE a wide spatula to remove fillets to a platter. Serve warm or at room temperature.