Lightly salt and pepper fillets. Heat oil in a large skillet. Add 2 tablespoons butter and heat. Lightly sauté fillets, flesh sides down, until golden brown, about 4 to 5 minutes. Turn over and repeat. Drain on paper towels. Keep warm.
While fillets are cooking, in a small saucepan combine broth and rum. Heat and simmer for 2 minutes. Add pineapple juice, 2 teaspoons butter, ¼ teaspoon salt, ⅛ teaspoon pepper and basil. Spoon over warm fish.
Contributed by Joyce Taylor