Put the trout in a dish, add the milk, and sprinkle with salt and pepper. Turn them several times to coat well. Set aside. Spread the flour over a flat dish. Remove the trout from the milk and dredge them in the flour. Shake off any excess flour. Heat half of the oil in a nonstick frying pan large enough to hold 3 trout in one layer. Cook them over medium heat for 4 minutes on one side. Turn them and cook for 6 to 8 minutes, or until brown. Transfer the trout to a warm platter and keep them warm. Repeat the process using the remaining oil and fish. Meanwhile, melt 1 TB. of the butter in a frying pan over high heat. Add the mushroom slices and sprinkle with salt and pepper. Saute them, stirring and shaking the pan, until the liquid has evaporated and the mushrooms are nicely browned. Arrange the mushrooms over the trout and sprinkle with the lime juice. Melt the remaining butter in a frying pan over high heat, shaking the pan, until the butter turns hazlenut brown. Pour it over the trout, sprinkle with the parsley, and serve immediately. ----