1. Wash the trout under cold running water, pat them dry and season them inside and out with the salt and a few grin dings of pepper. Spread the flour on one piece of wax paper and the cornmeal on a separate piece; break the eggs into a shallow bowl and beat them to a froth with a fork.
2. In a heavy 12-inch skillet, heat the oil over moderate heat until a light haze forms above it. Roll each trout in the flour, immerse it in the egg and then turn it about in the cornmeal to coat it evenly.
3. Fry the trout in the hot oil, two at a time, for 4 to 5 minutes on each side, or until they are golden brown. Drain the trout briefly on paper towels, then place them on a heated platter.
4. Melt the butter over moderate heat in a separate skillet, stirring so that the bits melt without browning. Remove the pan from the heat, stir in the lime juice, chives and parsley, and taste for seasoning. Pour over the trout and serve at once.
