Bring a medium saucepan of water to a boil. Remove from heat. Place rice vermicelli in the water and soak 3 to 5 minutes, until soft. Drain and rinse with cold water.
Cut the shrimp in half. Fill a large bowl with hot water. One by one, dip the rice wrappers in the water for a few seconds to soften. Lay wrappers flat and place desired amount of shrimp, carrot, lettuce and basil in the center. Roll the edges of the wrappers slightly inward. Beginning at the bottom edge of each wrapper, tightly wrap the ingredients.
In a small bowl, mix the hoisin sauce with water until desired consistency had been attained. Heat the mixture for a few seconds in the microwave.
Serve the spring rolls with the warm fish sauce mixture.