1. In a medium bowl, cover the vermicelli with cool water and let soak until pliable, about 20 minutes.
2. Meanwhile, in a saucepan of boiling water, cook the shrimp until bright pink, 1 to 2 minutes. Using a slotted spoon, transfer the shrimp to a colander. Rinse under cold water and pat dry. Halve the shrimp lengthwise; cover and refrigerate.
3. Bring the water back to a boil. Add the drained vermicelli and cook, stirring, until al dente, about 1 minute. Drain and rinse until completely cool. Let the vermicelli dry in the colander for about 20 minutes, tossing occasionally.
4. Dip each rice paper in a bowl of cool water to wet it. Set the rice paper on a work surface to soften; the paper will become opaque and pliable. Pat dry. Put 4 shrimp halves, cut side up, in a line across the lower third of each rice paper. Top with 2 or 3 sprigs of watercress, a large pinch of shredded carrot, 2 strips of red pepper and some of the vermicelli. Press to flatten, then top with a slice of avocado. Pull the rice paper up and over the filling and roll up tightly, folding in the sides as you go. Place the roll on a large platter, seam side down, and repeat with the remaining ingredients. When all the summer rolls are made, cut them in half crosswise and arrange, cut side up, on the platter. Serve the summer rolls with the Herbed Nuoc Cham for dipping.
Make Ahead: The summer rolls can be tightly wrapped in plastic and refrigerated for up to 1 hour.
Wine Recommendation: The brisk acidity and bright, tangy fruit of an Italian Pinot Grigio would play off the spicy watercress in these rolls and the citrusy lime sauce. Look for the 1998 Colterenzio Alto Adige or the 1998 Ronco del Gnemiz Fruili.