In a large stockpot, stir together the chicken stock, sesame oil, rice wine vinegar, soy sauce, and garlic chili sauce.
Bring to a boil, cover, and lower heat to a simmer for 15 minutes.
Add in the sliced mushrooms and continue to simmer with the lid on for 5 more minutes. Taste to season with salt and pepper.
Remove the lid and add in the asparagus tips and snap peas.
Simmer with the lid off for 3-4 minutes until the vegetables just begin to turn bright green and soften.
Turn the heat down to low and add in the chicken to just heat through.
Remove pan from heat and divide soup evenly between 4-6 soup bowls, depending on your crowd.
Evenly divide the rice noodles and eggs amongst the bowls, then garnish each with the red chili pepper, cilantro leaves, green onions, and sesame seeds.