Put carrots, celery, onions, lemon slices, bay leaves, and peppercorns in a fish poacher or a large, deep roasting pan. Rub salmon with salt, then lay on top of vegetables. Add dill, parsley, white wine, and just enough water to cover.
Put poacher over two burners and bring to a simmer over medium heat. Cook until salmon is pink, about 35 minutes, then remove from heat. Let salmon rest in poaching liquid for 5 minutes, then transfer to a work surface, peel skin from one side, and scrape off dark flesh with a knife. Reserve poaching liquid to use in egg-caper sauce or other recipes calling for fish stock.
Lift off top filet of salmon, transfer to a platter, then remove salmon backbone and any other visible bones. Turn fish over, and peel skin and scrape off dark flesh as in step 2, then transfer remaining filet to platter. Serve warm with egg-caper sauce.
EGG-CAPER SAUCE: Melt butter in a small heavy saucepan over medium heat. Add flour and cook, whisking constantly, until mixture is bubbling, about 2 minutes (do not brown). Slowly whisk in fish stock and heavy cream. Bring to a simmer and cook for 30 seconds, then remove from heat and set aside to cool for 5 minutes. (Sauce will thicken as it rests.) Stir in eggs and capers. Season to taste with salt and pepper. Keep warm over low heat and serve with poached salmon. Makes 2 cups.