In a bowl or cup, add 1 egg yolk, 1 tbsp kewpie mayo, and the ramen seasoning packet. Use a whisk or fork to mix this until it is a smooth paste and fully combined.
Bring a pot of water to a boil and add the ramen noodles. Boil according to package instructions until cooked to your liking. Take hot water from the pot, 1 tablespoon at a time, and add it to the bowl of sauce, whisking to combine. Add 2-3 tbsp of hot water total. Drain the noodles of about 90% of their remaining water, then return to pot off the heat.
To the noodles in the pot, add 1 tbsp salted butter along with the yolk/mayo/seasoning sauce. Stir until well combined and butter is melted. Add 1 slice of american cheese or about 2-3 tablespoons of mild shredded cheddar cheese. Stir until fully melted.
Pour the pot of noodles into a bowl, then garnish with generous amounts of sliced scallions, a drizzle of chili oil, and a poached or soft boiled egg.