Peel the onions by plunging them into boiling water for a few moments then slipping off the skins. Melt the butter in a large low-sided pan, add the mushrooms and onions and cook for 5 minutes. Add the thyme sprigs, bay leaves, wine and seasoning, and simmer gently for 5 minutes. Carefully place the halibut steaks in the pan, baste with red wine, cover and cook for about 6 minutes. When the fish is ready, the central bone will come out easily if pulled. Lift the fish out of the pan onto serving plates.
With a slotted spoon, remove the onions and mushrooms and arrange on the plates with the fish. Remove the thyme and bay leaves and discard. Take the pan from the heat and add the arrowroot, mixing well, then stir in the parsley and spoon the sauce over the fish.