Lightly coat a large, nonstick frying pan with cooking spray. Over high heat, saute the strips of steak until slightly pink, about 5 minutes. Set aside on a covered platter to keep warm.
Fill a large pot 3/4 full with water and simmer. Add the soba noodles and cook until almost tender, about 10 minutes, or according to package directions. Drain the pasta thoroughly. Rinse the noodles and drain again.
Meanwhile, in a large pot fitted with a steamer basket, bring 1 inch of water to a boil. Add the asparagus and broccoli florets, cover and steam until tender, about 10 minutes. Add the vegetables to the noodles and toss gently to mix evenly.
To make the sauce, in a small saucepan over medium heat combine the soy sauce, rice wine vinegar, sesame oil, ginger, sugar and pepper. Heat until warmed.
Divide the noodle-vegetable mixture onto warmed plates. Add the strips of steak and drizzle with the sauce. Serve immediately.