Cook pasta following package directions. Drain and rinse briefly under cold water.
Meanwhile, heat an outdoor grill or a stovetop grill to medium-high. Place mushrooms, red and yellow peppers and scallions in a large bowl. Toss with peanut oil and season with salt and pepper. Grill vegetables for about 3 minutes per side. If using an outdoor grill, use a grilling basket to keep vegetables from falling through the grates.
In a small bowl, whisk soy sauce, vinegar, sesame oil and sugar. Place pasta and vegetables in a large bowl; toss with dressing. Spoon vegetable mixture over greens and serve immediately.