In large heatproof glass measure or bowl, combine boiling water, salt, brown sugar, granulated sugar, onion and ginger; stir until salt is dissolved. Add cold water; let cool. Add dill sprigs.
Trim 1 inch (2.5 cm) off thinner long edge of fish; remove any remaining pin bones along centre. Place fish, flesh side down, in large shallow glass or ceramic dish, folding over thin tail end if necessary to fit. Pour in brine mixture to cover; weigh down fish with plate(s) to keep submerged. Cover and refrigerate for 4 hours.
Remove fish from brine; rinse, pat dry and place, skin side down, on rack.
Sprinkle with pepper, coriander, and dill. Refrigerate until flesh is tacky to the touch, 1 to 2 hours. (Make-ahead: Wrap and refrigerate for up to 24 hours.)
Meanwhile, soak 2 cups wood chips in water for 1 hour; drain. Set foil drip pan under one rack of two-burner barbecue or under centre rack of three-burner barbecue. Heat opposite burner(s) to medium-low. Seal soaked chips in foil to make packet; poke several holes in top.
Place over lit burner. (For charcoal grill, set drip pan under one side of grill and arrange hot coals on other side. Place packet directly on coals.) Close lid and let smoke fill barbecue.
Place fish, skin side down, on greased grill over drip pan; cover and smoke until fish flakes easily when tested, about 1-3/4 hours. (If skin sticks to grill, slide fish off skin onto platter.) Serve with lemon wedges.
