1. Combine the fish trimmings, onions, parsley sprigs, bay leaf and peppercorns in a 6- to 8-quart enameled or stainless-steel pot. Pour in the wine and water and, stirring occasionally, bring to a boil over high heat.
2. Reduce the heat to low and simmer, partially covered, for 30 minutes. Then strain the stock through a fine sieve set over a deep bowl or saucepan, pressing down hard on the fish trimmings and vegetables with the back of a spoon before discarding them.
3. In a heavy 4- to 5-quart enameled or stainless-steel casserole, melt the 2 tablespoons of butter over moderate heat. When the foam subsides, stir in the celery. Cover tightly and reduce the heat to low. Simmer 5 minutes.
4. When the celery is soft but not brown, spread the pieces of eel, perch, pike and carp evenly on top, and dot the fish with the bits of butter. Pour in 6 cups of the strained fish stock and add the crumbled thyme.
5. Bring to a simmer over high heat, then reduce the heat to low and cover the casserole tightly. Simmer for 6 to 8 minutes, or until the flesh flakes easily when it is prodded gently with a fork. Do not overcook the fish.
6. With a slotted spoon or spatula transfer the pieces of fish to a heated tureen. Bring the stock remaining in the casserole to a boil over high heat and cook briskly, uncovered, for 6 to 8 minutes, or until it reaches the intensity of flavor you like.
7. Taste the stock for seasoning, pour it over the fish in the tureen and serve at once.
