Soak the glass noodles. Place the dried glass noodles in a bowl and cover with lukewarm water. Let soak until softened, then drain well and cut into shorter pieces.
Make the dipping sauce. Combine the water, rice vinegar, sugar, and salt in a small saucepan and bring to a gentle boil over medium heat, stirring until the sugar dissolves. Simmer for about 5 minutes until slightly thickened, then remove from the heat. Add the chili, carrot, and peanuts just before serving, reheating briefly if needed.
Mix the filling. In a large bowl, combine the ground pork, softened glass noodles, vegetables, egg, and all seasonings. Mix gently until evenly combined, being careful not to overwork the mixture.
Fold and seal the rolls. Place a small amount of filling near the bottom corner of a wrapper. Roll over the filling snugly but not too tightly, fold in the sides, then brush the top sides with egg. Finish rolling upward and press gently to seal. Repeat with the remaining wrappers and filling.
Deep-fry. Heat oil in a deep pan until hot but not smoking. Fry the rolls in batches, turning as needed, until golden and crisp. Drain briefly on a rack or paper towel.
Serving tip. Serve hot with fresh herbs like cilantro, mint, and basil. Wrap a piece of the roll in lettuce with herbs and dipping sauce, and eat in one bite.