In the base of a fish poacher (with rack removed), or large stainless steel roasting pan, place the ½ each of the wine, fish stock, vegetables, garlic and butter, sprinkling half the parsley over all. Place the rack back into the fish poacher, or if using a roasting pan, place a cooling rack onto the bottom of the pan. Place the fish on top of the rack, then cover with the remaining half of the vegetables and butter, pouring the rest of the liquid and parsley over all. (The liquid should come just up to the rack. If you need to add more liquid, add it in equal parts fish stock to wine.)
Bring the liquid to a boil, then reduce heat to a gentle simmer. Cover with lid, or a tight fitting piece of aluminum foil. Cook until fish is opaque, about 10 minutes for every inch, as measured at thickest part of the fish. (See not above.)
Gently lift rack from poacher or roasting pan, carefully sliding fish onto a serving platter. Spoon sauce and vegetables on and around fish and sprinkle with parsley to serve.