To prepare dressing, combine first 5 ingredients, stirring with a whisk.
To prepare salad, cook cellophane noodles according to package directions. Drain and rinse with cold water; drain. Set aside.
Combine water, salt, and eggs, stirring with a whisk. Heat 1/2 teaspoon oil in a small nonstick skillet coated with cooking spray over medium-high heat. Pour half of egg mixture into pan; quickly tilt pan in all directions so egg mixture covers pan with a thin film. Cook 1 minute or until done. Place cooked egg on a cutting board. Repeat procedure with remaining egg mixture and oil. Cut egg rounds in half, and cut into thin strips.
Arrange 1/2 cup cellophane noodles, 1/3 cup cucumber, 1/3 cup carrot, 1 tablespoon peanuts, 2 teaspoons cilantro, and 2 teaspoons basil in separate piles on each of 6 plates. Serve each salad with about 3 tablespoons dressing.