Trim fat from steak. Cut steak diagonally across grain into thin slices.
Combine ginger, salt, and pepper; toss with steak.
Coat a large nonstick skillet with cooking spray; place over medium-high heat until hot. Add half of beef, and cook 3 minutes, stirring often. Remove beef from pan. Set aside in a large bowl; keep warm. Repeat with additional cooking spray and remaining beef.
Coat pan with cooking spray; add red pepper, and cook 2 minutes. Add red pepper to beef strips; toss well.
Combine coleslaw and peanut dressing in a large bowl; stir well. Top coleslaw mixture with beef mixture. Let chill. Toss well before serving.