In a large skillet, melt 1 tablespoon of the butter. Add the sage leaves and cook over moderate heat, turning once, until crisp, about 2 minutes per side. Transfer the sage leaves to a plate lined with paper towels to drain. Add 1/4 inch of the vegetable oil to the skillet and heat until shimmering. Carefully add the trout fillets and fry over moderately high heat until golden brown and just cooked through, about 3 minutes per side. Divide the fillets among 4 plates.