Preheat oven to 450°.
Snap off tough ends of asparagus, and cut asparagus into 2-inch pieces. Arrange asparagus, mushrooms, and green onions in a single layer on a broiler pan coated with cooking spray. Bake at 450° for 8 to 10 minutes or until golden brown, stirring once.
Cook pasta according to package directions, omitting salt and fat. Drain, reserving 3 tablespoons pasta water.
Add roasted vegetables, reserved pasta water, and chicken to pasta; toss gently.
Combine olive oil, 2 tablespoons hot water, balsamic vinegar, and pepper; stir well with a whisk. Add to pasta mixture, and toss well. Sprinkle with cheese. Serve immediately.