Make Noodles: Follow the instructions on the package of noodles for cooking. Finish cooking noodles before starting on the chicken. Rinse noodles well under cold water.
Make sauce: Mix together in a small bowl: vinegar, fish sauce, sugar, peanut butter, and paprika.
Make chicken: Heat olive oil in a wok or large heavy skillet. Add garlic, red pepper flakes, and chicken; sauté chicken until browned. Remove from wok and set aside.
Heat safflower oil in wok over medium-high heat. (if not making chicken, add garlic and red pepper flakes to the oil and sauté for a minute until garlic is fragrant)
Crack eggs into a small bowl (to ensure no shells get into the meal). Pour eggs into the hot oil, stirring to break the yolks and half-scramble, and cook until firm.
Add sauce and carrots and cook for 3-4 minutes, stirring occasionally.
Add cooked noodles and stir gently so they don't break up. Adjust seasonings to taste.
Sprinkle crushed nuts and chopped green onions over the top and serve with a lime wedge.