Bring a medium pot of water to a boil. Reduce to a simmer. Add shrimp; cook until pink and cooked through, about 2 minutes. Slice cooked shrimp in half lengthwise. Cool, then toss with lime juice and a few pinches of salt. Set aside.
In a medium bowl, cover rice vermicelli with hot water by 2 inches; let soak for 10 minutes. Drain, and rinse under cold water. Toss with basil, cilantro, rice vinegar and sesame oil. Set aside.
Have all ingredients ready for rolling the spring rolls: carrot, mango, seasoned rice noodles, shrimp, asparagus and mint leaves.
Fill a dish or your kitchen sink with warm water. Working with 1 rice-paper wrapper at a time, soak in water for 30 seconds; immediately lay flat on a damp towel. Smooth to remove wrinkles, than fold up the bottom quarter toward the top. Working with your hands, place about two tablespoons of the rice noodles on the folded up part of the wrapper. Place a few asparagus spears, carrot, mango and shrimp on top of the noodles. Add a mint leaf slightly above the rest of the filling.
Fold sides of the wrapper in toward the middle and roll the summer roll up, keeping the filling tightly pressed together. Tuck a few mini chives in to the side before you roll it all the way. Place roll on a plate and cover with a damp towel.
Repeat with remaining rice-paper sheets and filling. Chill summer rolls until ready to serve. Slice summer rolls in half to show the vibrant colors inside and serve with avocado puree or peanut sauce.