Bring a large pot of water to a boil. Add the noodles and cook as the label directs; drain and rinse with cold water.
Meanwhile, whisk the lime juice, fish sauce, brown sugar, garlic, chili sauce and 1/3 cup water in a medium bowl. Transfer 1/4 cup of the marinade to another bowl and toss with the shrimp. Toss another 1/4 cup marinade with the asparagus and mushrooms in a third bowl. Let the shrimp and vegetables marinate 10 minutes at room temperature. Toss the noodles with the remaining marinade.
Heat a grill or grill pan to medium-high. Grill the shrimp, asparagus and mushrooms until the shrimp is just cooked through and the asparagus is slightly tender, 2 to 3 minutes per side. Halve the mushrooms and cut the asparagus into pieces.
Divide the noodles among bowls and top with the shrimp, asparagus, mushrooms, carrot and cilantro.
Photograph by Antonis Achilleos
Recipe courtesy of Food Network Magazine