Bring a medium saucepan of water to a boil over high heat. Add the shrimp and cook until bright pink and just opaque, about 1 1/2 minutes. Drain in a colander and run under cold water until cool. Pat the shrimp dry with paper towels and place on a cutting board. Cut shrimp in half horizontally. Place in a medium bowl, cover with plastic wrap and refrigerate until ready to wrap.
Meanwhile, place noodles in a heatproof baking dish, cover with hot water, soak 8–10 minutes, drain and rinse under cold water.
Arrange all remaining ingredients in bowls around prep area.
Place a clean, damp kitchen towel on a work surface. Place 1/2 inch of cool water in a pie plate. Working with 1 wrapper at a time, completely submerge the wrapper until it is soft and pliable, 10–15 seconds. Remove the wrapper from the water and place it on the towel.
Working quickly, place 4 shrimp halves, cut side up, in a straight row across lower third of spring roll skin. Top shrimp with 2 basil leaves, 2 mint leaves, a sprig of cilantro, a few tablespoons of shredded cabbage, a few cucumber sticks, a pinch of carrots and 1/4 cup rice noodles.
Carefully lift edge of spring roll wrapper nearest you up and over filling. Fold sides over filling if desired and continue to roll away from you until edges are sealed, rolling as tightly as possible without tearing the wrapper. Transfer rolls to a platter, cover with a damp paper towel and continue building remaining rolls.