Notes: If apple cider is unavailable, substitute apple juice and increase the amount of cornstarch to 1¾ teaspoons. Use the bottom of a small saucepan or skillet to smash the ginger. To ensure uniform cooking, buy a 1½- to 2-pound center-cut salmon fillet and cut it into four pieces. If your salmon is less than 1 inch thick at its thickest point, check for doneness after 10 minutes of roasting in step 3.
Adjust oven rack to middle position and heat oven to 300°F. Dissolve salt and ¼ cup sugar in 2 quarts cold water in large container. Submerge salmon fillets in brine and let stand at room temperature for 15 minutes. Remove fillets from brine and pat dry with paper towels.
Meanwhile, combine cider, vinegar, sugar, soy sauce, and cornstarch in small saucepan and stir until no lumps remain. Add ginger and bring to simmer over medium-high heat, stirring frequently. Continue to cook, stirring frequently, until thickened, about 1 minute longer. Remove from heat and let ginger steep for at least 5 minutes. Discard ginger and transfer 2 tablespoons glaze to small bowl.
Heat oil in 12-inch ovensafe nonstick skillet over medium-high heat until just smoking. Place fillets, flesh side down, in skillet and cook until flesh side is well browned, 2 to 3 minutes. Flip fillets and reduce heat to low. Brush tops of fillets with reserved 2 tablespoons glaze. Transfer skillet to oven and cook until centers are still translucent when checked with tip of paring knife and register 125 degrees (for medium-rare), 10 to 15 minutes. Wash and dry brush.
Brush remaining glaze on top and sides of each fillet and sprinkle with chives or parsley. Transfer to platter or individual plates and serve.
