Broil beef for 6-8 minutes on each side. Meanwhile, in a small saucepan or microwave-safe bowl, combine the remaining ingredients. Cook until preserves are melted. Set aside 1/2 cup; brush remaining sauce over steak.
Broil 2-3 minutes longer or until meat reaches desired doneness (for medium-rare, a meat thermometer should read 145°; medium, 160°; well-done, 170°). Slice meat on the diagonal; serve with reserved apricot sauce.