Preheat the oven to 425°. In a small bowl, beat the butter, basil, garlic and lemon juice until well combined. Set aside. Parboil the potatoes and baby carrots for 5 minutes. Drain. Divide the fillets into 4 equal al portions.
Place the fillets in abuttered 9x13" pan, or an attractive gratin dish with the same volumn. Arrange the vegetabes over the fish in an appealing pattern. Top each fish portion with one-fourth of the butter-garlic mixture. Ciover tightly with aluminum foil. Bake for 20-30 minutes or until the fish flakes easily with a fork. Serve immediately.