For Nuoc Cham dipping sauce
5½ tablespoons sugar
¾ cup warm water
¼ cup plus 1 tablespoon Asian fish sauce (preferably from Phu Quoc)
2 tablespoons rice vinegar (not seasoned)
2 teaspoons fresh lime juice (optional)
2 garlic cloves, minced
2 fresh Thai chiles (2 to 3 inches; preferably red; including seeds), thinly sliced crosswise

For spring rolls
7½ oz very thin bean thread noodles (in small skeins, also known as cellophane or mung bean noodles*)
2 oz dried wood ear mushrooms
1 medium shallot
2 garlic cloves
2 cups grated carrots (4 to 5 carrots)
1 lb ground pork shoulder
¼ cup Asian fish sauce (preferably from Phu Quoc)
¼ cup plus 1 teaspoon sugar
2½ teaspoons black pepper
2 teaspoons salt
1 lb shrimp in shell, peeled and deveined
25 (8-inch) spring roll wrappers
1 large egg yolk, lightly beaten
About 6 cups vegetable oil

Make dipping sauce:

Stir together sugar and water until sugar is dissolved. Stir in remaining sauce ingredients, then chill, covered, at least 2 hours.

 

Prepare filling:

Put noodles in a large bowl and cover with hot water by several inches. Soak, pulling noodles apart and stirring occasionally, 10 minutes. Drain noodles and cut into 2- to 3-inch pieces (you should have about 3 cups), then transfer to another large bowl.

 

Put mushrooms in a bowl and cover with hot water by several inches. Soak 15 minutes. Drain and rinse mushrooms thoroughly, then drain again. Trim off and discard any hard parts from mushrooms. Finely chop mushrooms. (You should have about 2 cups.) Add to noodles.

 

Pulse shallot and garlic in a food processor until finely chopped, then add to noodles along with carrots, pork, fish sauce, sugar, pepper, and salt. Pulse shrimp in processor until coarsely ground. (Do not over process or it will become pasty.) Add shrimp to noodle mixture. Mix with your hands until well combined. Chill filling, covered with plastic wrap, until cold.

 

Assemble rolls:

Line 2 trays with wax paper.

 

Transfer one fourth of filling to a small bowl and keep remainder chilled, covered.  Place 1 wrapper on a work surface, keeping remaining wrappers covered with a clean kitchen towel (to prevent them from drying out).  About 1" up from the bottom of the wrapper put 2 tablespoons filling along middle of the wrapper 1" up from the bottom and shape filling into a thin 5-inch log. Fold left and right corners of wrapper over filling, overlapping slightly and aligning bottom edges. (Wrapper will resemble an open envelope.) Dab top corner with yolk, then roll up wrapper away from you into a long thin roll, making sure ends stay tucked inside.  Place on a tray, seam side down.  Repeat with remaining triangle. Make more rolls in same manner with remaining wrappers and filling, keeping trays of rolls chilled, loosely covered, until ready to fry.  (See pictures below of how to place filling and roll the wrapper).

 

Heat 1½ inches of oil in a 5- to 6-quart pot over moderately high heat until it registers 365°F on thermometer.  Fry rolls in batches of 5 or 6, keeping rolls apart during first minute of frying to prevent sticking, until golden brown and cooked through, 4 to 5 minutes.  (Return oil to 365°F between batches.)  Transfer as fried to a colander lined with paper towels and drain rolls upright 2 to 3 minutes.  To eat, wrap hot or warm rolls in lettuce leaves and tuck in mint and cilantro leaves.  Serve with dipping sauce.

 

Cooks' notes:

• Rolls can be assembled (but not fried) 1 month ahead and frozen, wrapped well in foil.  Thaw in refrigerator before frying.
• Sauce and filling can be made 4 hours ahead and chilled separately, covered.