Cook leeks in boiling water to cover 1 minute; drain. Plunge leeks into ice water to stop the cooking process; drain.
Rub a large skillet with 1 tablespoon butter, and sprinkle with shallots. Place fillets over shallots, and pour vermouth and chicken broth over fish. Sprinkle with 1/4 teaspoon salt and 1/4 teaspoon pepper. Arrange leeks around fish. Cover with buttered parchment paper. Bring liquid to a boil; reduce heat, and simmer 12 to 14 minutes or until fish flakes with a fork, basting occasionally. Remove fish from pan; keep warm.
Pour sauce through a wire-mesh strainer into a bowl, reserving leeks. Return liquid to pan, and bring to a boil; reduce heat, and simmer, uncovered, 2 minutes or until sauce is reduced to 3/4 cup. Add cream; bring to a boil. Reduce heat, and simmer 1 1/2 minutes or until sauce is reduced by half. Whisk in mustard, 2 teaspoons butter, and lemon juice. Stir in 1/2 teaspoon salt and 1/4 teaspoon pepper. Add reserved leeks, and cook 1 minute or until hot; spoon over fish.
Bayona, New Orleans