Heat oil in wok over medium heat. When oil reaches 350 degrees add the sliced ginger and fry until lightly brown and crispy, about 4 minutes. Remove to a plate lined with a paper towel and reserve as garnish. Carefully pour out half the oil from the wok into a heatproof container and reserve for frying egg.
Return wok to the stove and turn the heat up to high; add onion, carrot, ginger sticks and tofu. Stir-fry for about 2 minutes. Stir in chayote, fish sauce, sweet soy sauce and regular soy sauce and continue to cook for another 2 minutes. Add scallions, lime juice and egg noodles and stir. Cook until noodles are heated through and transfer to large serving bowl.
Add reserved oil to wok and heat over medium-high heat. Crack egg into a small bowl and carefully slide the egg into the hot oil. Fry for 3 minutes until egg white is cooked but yolk is still runny. Place egg on top of stir fry and garnish with scallions and fried ginger chips.
Recipe courtesy of Spike Mendelsohn