Trim fat from steaks. Combine hoisin sauce, wine, ginger, and 1 garlic clove in a shallow dish. Add the steaks; cover and marinate in refrigerator 2 hours, turning steaks occasionally.
Combine water and mushrooms in a saucepan; bring to a boil. Remove from heat; cover and let stand 30 minutes. Remove mushrooms from pan with a slotted spoon, reserving liquid. Discard mushroom stems; cut caps into quarters, and set aside. Bring mushroom liquid to a boil; cook until reduced to 1/3 cup (about 5 minutes). Remove from heat. Remove steaks from marinade; add marinade to reduced mushroom liquid; set aside.
Prepare grill or broiler.
Place steaks on grill rack or broiler pan coated with cooking spray; cook 6 minutes on each side or until desired degree of doneness. Set aside and keep warm.
Heat the sesame oil in a nonstick skillet over medium-high heat. Add mushrooms, green onions, and 1 garlic clove; sauté 2 minutes. Add marinade mixture, and cook 2 minutes.
Cut the steaks diagonally across grain into thin slices. Arrange steak on each of 2 plates, and top with mushroom sauce. Serve with cooked rice.
