1. Cut steak diagonally across grain into 16 thin slices. Combine steak, soy sauce, 1 tablespoon vinegar, mirin, and sesame oil in a shallow dish. Marinate steak 10 minutes, turning occasionally.
2. Remove steak from marinade, reserving marinade. Place 1 steak slice on a cutting board or work surface; arrange 3 green onion pieces and 3 bell pepper strips on the end of steak slice. Roll up; set aside, seam side down. Repeat procedure with remaining steak strips, onion pieces, and bell pepper pieces.
3. Heat a grill pan over medium-high heat. Coat pan with cooking spray. Place beef rolls in pan, seam side down; cook 7 minutes, turning once.
4. While beef rolls cook, bring reserved marinade to a boil over medium-high heat; cook 3 minutes. Remove from heat; stir in remaining 1 1/2 tablespoons vinegar. Drizzle sauce over rolls.
Spicy ginger noodles: Combine 3 cups hot cooked linguine, 1 tablespoon canola oil, 1 1/2 teaspoons grated peeled fresh ginger, 1 teaspoon dark sesame oil, 1/2 teaspoon salt, and 1/2 teaspoon crushed red pepper.