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Step 1
Prepare all the ingredients. Chop the kimchi and vegetables to desired sizes. Whisk the eggs in a bowl with water, salt and pepper, and gochugaru chili flakes.
Step 2
Prepare the broccolini: Add an inch of water to a medium saucepan, add the broccolini and place the lid on top. Let this steam for 5 minutes or until fork tender. Drain and then mix with 1 teaspoon sesame oil, 1 teaspoon butter and a pinch of salt. Set aside, once cool enough to handle, roughly chop.
Step 3
Meanwhile, to a well-seasoned medium heated pan, add butter. Once melted, add in the finely chopped white part of the green onion and the chopped kimchi. Cook for a couple of minutes or until softened, then add the whisked eggs. Reduce temperature to medium-low. Stir to combine.
Step 4
Let it sit the top surface of the eggs is thickened and no visible liquid remains, about 2 minutes, then add as much broccolini as you want. I added about 1+ cup which is a lot, but so delicious.* Add dollops of goat cream cheese around the pan. Top with a lot of cilantro and the green part of the green onion. Put the lid on for 2 minutes or until the cream cheese has melted a little.
Step 5
Gently fold the omelet in half and slide on to a plate. This omelet is enough for 2-3 people, so divide accordingly.
Step 6
Drizzle with a tiny amount of sesame oil, coarse sea salt, more cilantro and green onion for serving. I also added a lot of both regular and black sesame seeds. I think the perfect complement to these Korean eggs is a toast of sourdough bread with more goat cream cheese.