Japanese Marinated Soft Boiled Egg for Ramen (Ajitsuke Tamago)
from https://www.seriouseats.com/

Beef Ramen with Eggs, Bok Choy and Slivered Scallians
Perfectly seasoned soft-boiled eggs for the best homemade ramen. Split in half and resting on the noodles, they're an amazing accompaniment to enrich and flavor the ramen.
Why It Works
- Cooking at a bare simmer, around 190°F, keeps the egg whites from turning rubbery and tough.
- Paper towels keep the eggs fully engulfed by the marinade.
- A 4 to 12 hour window is perfect for intensely flavored but tender eggs.
1 cup water (about 8 ounces; 225g)
1 cup sake (about 8 ounces; 225g)
1/2 cup soy sauce (about 4 ounces; 115g)
1/2 cup mirin (about 4 ounces; 115g)
1/2 cup sugar (about 3 1/2 ounces; 100g)
6 large eggs
Combine water, sake, soy, mirin, and sugar in a medium bowl and whisk until sugar is dissolved, or use an equal amount of chashu broth (a broth from braising pork belly in soy sauce, sake, and mirin) instead. Set aside.
Bring 2 quarts of water to a boil in a medium saucepan over high heat. Pierce fat end of each egg with a thumbtack to make a tiny hole (this prevents them from cracking and eliminates the air bubble at the end). Carefully lower eggs into water with a wire mesh spider or slotted spoon. Reduce heat to maintain a bare simmer (about 190°F). Cook for exactly 6 minutes. Drain hot water and carefully peel eggs under cold running water (the whites will be quite delicate).
Transfer eggs to a bowl that just barely fits them all. Pour marinade on top until eggs are covered or just floating. Place a double-layer of paper towels on top and press down until completely saturated in liquid to help keep eggs submerged and marinating evenly. Refrigerate and marinate at least four hours and up to 12. Discard marinade after 12 hours [the marinade could be reused - I would bring it to a boil first and let cool]. Store eggs in a sealed container in the fridge for up to 3 days. Reheat in ramen soup to serve.