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 fully cooked (165F on meat thermometer). 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 chicken back to the wok and stir to combine.
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.