Bring a pot of water to a boil for the noodles. When the water boils, cook the noodles per the package instructions.
Combine the chicken stock, rice wine vinegar, and fish sauce in a small saucepan and place over medium-high heat. Meanwhile, crack the eggs into a small bowl, break the yolks, and lightly whip. When the stock comes to a heavy simmer, stir the egg into the stock using chopsticks. Stir constantly for 2-3 minutes.
In a wok, add the sesame oil and place over medium-high heat. When the oil is hot, add the green onion, ginger, garlic, and chili garlic sauce. Cook for 5 minutes, stirring occasionally.
Here's where logistics shine. Add the soy sauce to the wok to break up any bits that might have stuck. Then drain the noodles and stir them into the ginger-garlic-chili in the wok. Divide the noodles into two bowls and add the stock-and-egg mixture to the bowls.