To prepare the salad, place the onion, papaya, and carrots in a bowl and mix well. In another bowl, combine the chile sauce, garlic, sugar, fish sauce, vinegar, and lime juice. Adjust the seasoning. Pour the chile sauce mixture over the papaya mixture and toss well. Add the cilantro and mint and toss well. Garnish with the peanuts.
Squeeze any excess moisture out of the shrimp. In a small pan, heat the 1 tablespoon peanut oil and 2 teaspoons of the sesame oil over medium-high heat. Add the shrimp and saute for 3 to 4 minutes, until pink and starting to curl. Drain the shrimp in a colander and set aside. Bring a saucepan filled with water to a boil. Place the rice noodles in a bowl and pour the boiling water over them. Allow to soak for 5 minutes, until softened. Drain and set aside.
Preheat the oven to 450 degrees.
Mix together the shrimp, rice noodles, carrot, mayonnaise, remaining 1/2 teaspoon sesame oil, vinegar, sesame seeds, chile sauce, and salt. Add the cilantro and mix well.
To prepare the lumpia, lay a wrapper on a clean work surface with the point facing you. Spread 2 tablespoons of the shrimp mixture evenly on the bottom one-third of each lumpia wrapper. Brush all 4 edges with the egg wash. Fold the bottom up over the filling and fold in the sides toward the middle. Starting at the bottom, roll up to form a tiny bundle. Repeat with the remaining filling and wrappers. Brush with peanut oil.
Place the lumpia on a baking sheet and bake for 10 to 12 minutes, until golden brown.
To serve, place 1/2 cup of the salad on each plate. Cut the lumpia in half diagonally. Stand 4 pieces of lumpia, point up, on each plate around the salad.
Recipe courtesy of Beverly Gannon's The Hali'imaile General Store Cookbook (Ten Speed Press, 2000)