Pat fillets dry and rub flesh sides with cayenne, 1/2 teaspoon salt, and 1/4 teaspoon black pepper (total). Dredge in flour. Heat 1/2 stick butter in a 12-inch heavy skillet over medium heat until foam subsides, then cook trout, skin side down, until skin is golden-brown, about 4 minutes. Turn fish over and cook until just cooked through, 1 to 2 minutes more. Transfer to a plate with a slotted spatula and keep warm, loosely covered with foil. Pour off butter from skillet and wipe clean, then cook pecans with remaining 3/4 stick butter, 1/4 teaspoon salt, and 1/8 teaspoon pepper over medium heat, stirring occasionally, until golden-brown, about 2 minutes. Stir in lemon juice and parsley and spoon over trout.