In a 1- to 1 1/2-quart pan, bring 1 1/2 cups water, sugar, salt, ginger, bay leaves, and allspice to a boil. Stir until sugar dissolves. Remove from heat and let cool slightly.
Rinse salmon fillet, pat dry, and lay flat with skin down in a rimmed 12- by 15-inch pan. Pour sugar-salt mixture over salmon. Cover pan tightly and chill fish at least 4 or up to 24 hours, occasionally spooning brine over the fish.
Mound 16 charcoal briquets on the firegrate of a barbecue with a lid and ignite briquets. Or turn gas grill to high heat and close lid.
Meanwhile, add peppercorns to enough hot water to make them float; soak at least 15 minutes. Also add wood chips to enough warm water to make them float; soak at least 15 minutes.
Drain fish and discard brine. Rinse fish with cool water and pat dry. Set fish, skin side down, on a large sheet of foil; cut foil to fit outline of fish.
Rub honey over top of fish. Drain peppercorns and pat evenly onto fish to set them lightly in place.
When coals are dotted with gray ash, in about 20 minutes, push half to each side of firegrate.
Drain wood chips and scatter 2 tablespoons on each mound of coals. For gas grill, put 1/4 cup chips in a foil pan and set over heat. Cover barbecue, and heat until chips start to smolder, about 10 minutes.
Set grill 4 to 6 inches above the firegrate.
Place salmon on foil in center of grill (not directly over coals); if using gas, turn to lowest setting and adjust for indirect heat (parallel to sides of salmon, not beneath the fish).
Set an oven thermometer on top of the center of the fish. Cover barbecue. For charcoal, open vents 1/4 inch, and after 30 minutes add 3 briquets to each mound of coals; repeat every 30 minutes of cooking.
Check thermometer often to be sure temperature stays about 160°. If temperature drops, open vents for charcoal slightly, or turn up heat on gas grill. If temperature rises, close 1 or 2 of the vents, or open lid of gas grill, then prop open slightly. Add wood chips as needed to produce a faint, steady stream of smoke. Moisture that accumulates on fish will evaporate. Cook salmon until a thermometer inserted in center of thickest part reads 140°, from 1 hour to 1 hour and 15 minutes.
Using wide spatulas, slide fillet with foil onto a rimless baking sheet, then slide fish from sheet onto a platter. Serve salmon warm, cool, or chilled.
Garnish with onion and dill. Cut fish across grain into wide slices or bite-size chunks; lift fish off skin.
* Percent Daily Values are based on a 2,000 calorie diet. Your daily value may be higher or lower depending on your calorie needs.