Season flour with salt and pepper. Dredge both sides of fillets in flour. Shake off surplus flour.
Heat saute pan over medium heat. Add olive oil and 1/4 cup clarified butter. Add fillets, flesh side down, to pan. Cook 6 minutes. Turn, and cook the other side for 4 minutes. Remove fish from pan to platter. Strain cooking juices and set aside. Return fillets to pan, flesh side up.
Meanwhile, in another pan, add remaining clarified butter. On medium-low heat, add tomatoes. Then add garlic. Stir gently. Stir in 1/4 teaspoon tarragon, 1 teaspoon dill, and the parsley. Add 1-ounce of Pernod, wine vinegar, and salt and pepper. Simmer gently. Add fish juices. Increase heat to high.
Season fish fillets with remaining dill and 1/4 teaspoon tarragon. Add remaining Pernod to pan with fish and set aflame.
Stir in butter to sauce and pour over fish. Remove from heat, slide onto platter, and serve immediately.
Recipe courtesy of Las Brisas Acapulco, Acapulco, Mexico