Cover a baking sheet with aluminum foil and coat with cooking spray. Lay asparagus and mushrooms on pan and coat with cooking spray. Season with pepper.
Bake vegetables for 15 minutes. Place snow peas and garlic on pan and continue to bake 20 minutes longer of until all vegetables are soft. Let vegetables cool. Take garlic out and set aside and chop the other mushrooms.
Combine noodles and cold water in a bowl and let them soak 10 minutes, noodles should be soft and separated. Strain noodles and combine with vegetables in a large bowl. Mix in carrot, cucumber, and green onions.
Squeeze garlic insides into a bowl and whisk in soy sauce, vinegar, vegetable oil, chili oil, sugar, and gingerroot. Spoon dressing over vegetables and top with cilantro. Spoon mixture on lettuce-lined plates and garnish with lime wedges.