Heat a grill pan over medium-high heat. Rub steak with 2 teaspoons soy sauce; sprinkle with salt and pepper. Coat pan with cooking spray. Add steak to pan. Cook for 5 minutes on each side or until desired degree of doneness. Remove from pan; let stand 10 minutes. Cut steak diagonally across the grain into 1/2-inch-thick slices.
Heat oil in a large nonstick skillet over medium heat. Add ginger and garlic; sauté 1 minute, stirring occasionally. Add remaining 2 tablespoons soy sauce and edamame to pan; cook 2 minutes.
Combine vinegar and wasabi paste in a bowl, stirring until smooth. Place 1/2 cup edamame mixture on each of 4 plates. Top each serving with 3 ounces steak; drizzle each with 1 tablespoon vinegar mixture.