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1. Place steak in a self-sealing plastic bag set in a shallow dish. Set aside 2 tablespoons beer; in a small bowl combine remaining beer, mustard, Worcestershire, 1 teaspoon of the tarragon, the salt, and pepper. Pour beer mixture over steak in bag. Marinate in the refrigerator for 4 to 6 hours, turning occasionally.
2. Meanwhile, in a small skillet over medium heat, cook shallot in hot oil 5 minutes or until tender. Stir in reserved 2 tablespoons beer. Remove from heat. Cool 10 minutes. In a small bowl combine softened butter, shallot mixture, and remaining 1 teaspoon tarragon. Transfer to waxed paper, shape into a log. Wrap and freeze.
3. Preheat broiler. Drain steak; reserve marinade. Season steak with additional salt and pepper. Place steak on the unheated rack of a broiler pan. Broil 3 to 4 inches from heat to desired doneness, turning once, broiling 12 to 15 minutes for medium rare (145 degrees F) or 15 to 20 minutes for medium (160 degrees F). Transfer to platter. Tent with foil and let stand 5 minutes.
4. Place reserved marinade in a small saucepan. Bring to boiling. Reduce heat to medium and simmer, uncovered, 15 minutes (Do not overcook; marinade can become bitter).
5. To serve, slice steak into portions. Drizzle with some of the marinade reduction, and top each with a slice of frozen butter. Makes 2 to 3 servings.