In a heavy-duty resealable plastic bag, combine oil, lemon juice, garlic, Worcestershire sauce and pepper. Add steaks to bag. Press the air out of the bag, and seal tightly. Turn the bag several times to distribute the marinade; place the bag in a bowl and refrigerate 30 minutes, turning bag occasionally.
Heat a large oiled skillet over medium-high heat.
Remove steaks from marinade, discarding marinade. Place 3 steaks in hot skillet; cook 4 to 5 minutes on each side or to the desired degree of doneness. Remove steaks to a serving plate, and keep warm. Repeat process with remaining 3 steaks. Top each steak with 1 to 2 tablespoons Tarragon Melting Sauce.
In a bowl add all ingredients together and mix until smooth. Cover, and refrigerate.