Boil 2-3 cups of water in a pot and cook the Shin Ramyun noodles according to package instructions (about 4-5 minutes). You can add the veggie flakes to the pot or leave them out.
While the noodles are cooking, combine 1 egg, 1 tbsp Kewpie mayo, and ⅔ of the Shin Ramyun soup seasoning packet in a large bowl. Mix well until smooth and creamy.
Once the noodles are just cooked, ladle about 1 cup of the boiling noodle water into the bowl with the egg-mayo-seasoning mixture. Stir quickly to create a creamy broth (don't pour all the water at once to avoid scrambling the egg).
Add the cooked noodles to the bowl and stir to combine everything well.
Top with chopped green onions and a generous drizzle of chili oil.
For the eggs, boil for exactly 6 minutes then remove them to an ice bath to stop the cooking and make them easier to peel.
