Bring a pot of water to a boil. Blanch bean sprouts in the boiling water for approximately 30 seconds, then remove with a slotted spoon and drain well. When the water returns to a boil, add rice noodles. Cook until tender but firm, 3 to 5 minutes. Drain and rinse under cold water.

Whisk eggs in a small bowl; add a pinch of salt. In a separate bowl, stir together lime juice, ketchup, brown sugar, and fish sauce.

Heat oil in a wok or large skillet over medium-high heat. Add garlic and fry for a few seconds. Add pepper flakes and carrots; cook for 1 minute then remove from the wok.