Depending on the size of your salmon, put 1 or 2 cedar grilling planks (about 15 inches each) in a large dish or roasting pan (it?s OK if they overlap). Pour in the wine, then add enough water to cover (if not using wine, just use all water). Weight the plank down with a heavy pot so it is submerged. Let soak at least 2 hours, flipping it over halfway.
About 30 minutes before cooking, preheat a grill to medium (if your grill has a thermometer, it should register about 375 degrees F). Combine the brown sugar, lemon zest, rosemary, 4 teaspoons salt and 2 teaspoons pepper in a small bowl. Remove any pin bones or belly fat from the salmon. Rub the salt mixture all over the flesh side of the fish. Transfer to a baking sheet, loosely cover and refrigerate 30 minutes.
Drain the cedar plank and arrange on the grill. Place the salmon skin-side down on the plank (if your salmon is large, you?ll need to put 2 planks side by side); cover and grill until just cooked through, 12 to 18 minutes, depending on the thickness. Transfer the plank to a board and top the salmon with parsley.