For the marinade, in a medium bowl combine vinegar, oil, soy sauce, brown sugar, mirin and wasabi paste; mix well. Place steak in a large resealable bag. Add 1/2 cup of the marinade; seal bag and refrigerate 12 hours, turning bag occasionally. Cover and refrigerate remaining 1/2 cup of marinade until ready to use.
Coat grill rack with nonstick cooking spray. Preheat grill to medium (300°F to 350°F). Remove steak from marinade; discard marinade. Grill steak 5 minutes per side for medium-rare (145°F) or to desired doneness. Remove steak from grill; let stand 10 minutes.
Meanwhile, for the sauce, pour reserved 1/2 cup marinade into a small saucepan. Bring to boiling over medium heat. Cook 8 to 10 minutes, stirring occasionally or until thickened. Slice steak across the grain into thin slices and transfer to a platter; drizzle with sauce, and serve.