Heat oil in a large nonstick skillet. Add ginger, pepper, and garlic; cook 1 minute. Add mushrooms; cook 2 minutes. Add vinegar and next 5 ingredients (vinegar through sugar); remove from heat.
Snap off tough ends of asparagus; remove scales with a knife or vegetable peeler, if desired. Brush asparagus with mushroom vinaigrette; keep remaining vinaigrette warm.
Prepare grill or broiler. Grill or broil the asparagus 3 minutes or until lightly browned. Place asparagus on pasta, and top with remaining mushroom vinaigrette.