Whisk together lime juice, hoisin sauce, and sugar. Set aside.
Peel and grate carrot. Peel, remove seeds, and grate cucumber. Remove seeds and membrane of jalapeño, mince. Mince garlic. Chop peanuts.
Fill large pot with water and salt, bring to boil. Add noodles, cook 2 to 3 minutes or until tender. Drain and run under cold water. Transfer noodles to bowl and drizzle 2 tablespoons of lime juice mixture over noodles. Toss to coat.
In separate bowl, mix carrot, cucumber, jalapeño, and peanuts. Drizzle with remaining lime mixture.
Fill large bowl with cold water. Place each dried rice paper wrapper in water for 30 seconds. Gently remove from water and lay flat. Layer cilantro leaves, carrot mixture, and noodles in center. Fold both ends up and roll tightly. Arrange seam side down on serving plate. Cover with towel until ready to serve.
In small saucepan, combine garlic, pepper flakes, and oil. Simmer 2 minutes. Add hoisin sauce, peanut butter, tomato paste, and water. Simmer 2 minutes. Serve as dipping sauce with spring rolls.