In a heavy bottom saucepan, heat 4 cups (1000 ml) water and bring to boil.
Once boiling, turn off the heat. Add 1 cup (250ml) cold water and gently submerge the cold eggs in the hot water. Cover the pot and take out the eggs gently after 17 minutes. Submerge the eggs into a bowl of cold water. Set aside for at least 5 minutes before cracking the eggs.
Broth
Add dashi to the frying pan and bring it to boil. Season with soy sauce, mirin, sugar, and salt. Taste and adjust the seasoning. Set aside.
Put the cooked udon noodles into the serving bowls. Pour the broth over the udon noodles. Crack an onsen tamago over the udon and sprinkle with green onion. Serve hot.
Notes
You can store the leftover onsen tamago for 1-2 days in the refrigerator, but they are still the best when eaten freshly cooked.To reheat, take out the onsen tamago from the fridge to room temperature and submerge them in 160F/70ºC for 10 minutes.