Cook the rice noodles according to package instructions. Drain and rinse in cold water. Using kitchen shears, cut the noodles into small pieces.
Set a medium saucepan of water of high heat and bring the water to a boil. Add the shrimp and cook until the shrimp are just cooked through, 60 to 90 seconds. Drain and immediately transfer to a bowl of ice water to stop the shrimp from cooking further. Drain and cut the shrimp in half lengthwise.
Fill a shallow baking dish with hot water. Working with 1 spring roll wrapper at a time, soak the wrapper in the hot water until soft. Place the wrapper on a cutting board.
Lay 1 shrimp half, 1 slice of avocado, ¼ cup of the noodles, 2 bell pepper half slices and a sprinkling of basil into the middle of the wrapper. F
old in the sides and roll tightly. Repeat with remaining wrappers and ingredients. Cut the rolls in half, if desired. Serve with soy sauce or a store-bought gyoza sauce.