Rinse the scallion
Rinse the Green Onion under cold water, checking between the layers near the green tops where grit can hide. Shake off the excess water and pat it dry so it will slice cleanly.
Slice it thin
Trim off the root end, then slice the scallion very thinly. Keep most of it for the egg mixture and set aside a small pinch for the top so the finished gyeran jjim looks fresh and bright.
Whisk the eggs
Crack the eggs into a bowl and whisk until the yolks and whites are completely blended with no streaks left. Pour in the Anchovy-Kelp Stock, Fish Sauce, and Sea Salt, then whisk again until smooth. Stir in most of the sliced scallion, saving that little pinch for garnish.
Cook gently
Pour the egg mixture into a small lidded saucepan or Korean earthenware pot. Set it over medium-low heat and stir slowly for 1 to 2 minutes, just until tiny soft curds begin to form around the edges. Reduce the heat to low, cover, and cook for 7 to 9 minutes until the eggs are puffed, softly set, and still a little jiggly in the center.
Finish and serve
Take the pot off the heat and let it sit for 1 minute so the center can finish setting. Drizzle the top with Toasted Sesame Oil, scatter over the reserved scallion, and serve right away while it is hot, fluffy, and spoon-soft.
