Prep the vegetables: Thinly slice the green onions, separating the whites and green. Finely chop the garlic cloves. Thinly slice the chili peppers (if using).
Make the seasoning paste: Combine all the ingredients in a small container and mix well.
Fill a pot with 8 cups of water and bring it to a boil. Carefully lower in the eggs. Once all the eggs are in, give them a few gentle stirs with a ladle. ( This will help keep the yolks nice and centered.)
Let the eggs boil gently for 7 minutes. Then, transfer them to an ice water bath to cool. Peel the eggs and set them aside.
In a large pan, heat the oil over medium-high heat. Once it gets nice and hot, add the ground beef. Spread it out and let it sear for 1 minute or until the bottom is nicely browned. Flip, break up the beef, and cook for 1 to 2 minutes or until no longer pink.
Add the white parts of the green onions and garlic. Stir-fry for 1 minute or until fragrant.
Reduce the heat to low. Add the seasoning paste and saute for 2 minutes. Be careful not to burn it. (If you're worried about burning, turn the heat off and saute using residual heat, or add a splash of water.)
Pour in the 2 cups of water. Stir well and bring it to a boil. Reduce the heat to medium-high and add the eggs. Let them simmer in the sauce for 7 minutes.
Turn the heat off. Add the remaining green onions, chili peppers (if using), sesame oil, and sesame seeds. Give everything a final mix.
To serve, scoop the egg(s) from the sauce and place them over hot steamed rice. Drizzle with extra sauce from the pan and a touch of sesame oil. Enjoy!
