Gut, clean and bone the trout. Wash, pat-dry and set aside. Chop the shallots, mushrooms and parsley. Salt to taste, add peppercorns and half of the butter cut into pea-size pieces.
Prepare a smooth mixture, then stuff the fish with it. Put the onion, the carrot and celery cut into pieces into a fish poacher. Lay the trout on top and cover with red wine. Cook over low heat. When the trout is done, remove from poacher, skin, place in a serving platter, and keep warm.
Filter the cooking liquid. Let it reduce a bit then add the butter whisking vigorously to prevent separation, and cook until the sauce is very hot. Adjust seasoning, pour the sauce on the trout and serve immediately.