Combine the sauce ingredients in a small bowl and mix well.

Heat the butter (or oil) in a large skillet over medium-high heat until hot. Add the kimchi and onions. Stir fry for 30 seconds to 1 minutes to draw out excess moisture from the kimchi.

Add the rice. Stir and chop to break it up with a spatula. Cook until the kimchi and onions are evenly mixed through the rice.

Add the sauce and frozen vegetables. Cook and stir until the rice is evenly coated and the vegetables are fully thawed. Divide the rice into 2 even portions and transfer to 2 separate plates.

Add 2 (or 3 if using) eggs into separate small bowls. Add half the salt and milk/cream (if using) to each bowl. Beat the eggs until they’re evenly mixed but not foamy.

Spray a medium-sized (9”) nonstick pan (*Footnote 3) with a thin layer of oil. If not using oil spray, add 1 teaspoon oil to the pan and use a paper towel to wipe the pan evenly with oil. Heat the pan over medium heat until the pan is warm.

Add the eggs and immediately begin scrambling using a spatula. Scramble for 20 to 30 seconds, or until the bottom is just set and the top is still runny. Then cook undisturbed to let the eggs set for 30 seconds, or until the top of the eggs become thick and creamy, but not fully set. If the eggs are still too runny, you can also cover the pan with a lid, turn off the heat, and let it steam for 20 to 30 seconds. This step helps the eggs to set slowly without burning the bottom.

Work on one omurice at a time.

Shaping method 1: Shape the plated rice into a long (American) football shape using a spatula. Put the skillet with the omelet near the plate and use a swift motion to flip the egg onto the rice, runny side down. Use two layers of paper towels to cover the egg, then use your hands to shape the dome, gently pressing the rice together. One side at a time, tuck both sides of the omelet to slide it under the rice.

Shaping method 2: Add half of the rice to one side of the omelet as if you were filling a Western-style omelet. Then fold the other half of the omelet over it. Carefully flip the omelet onto a plate so that the seam is facing down.

Shaping method 3: Add half of the rice into a small bowl and press it to mold the rice into a dome. Flip the rice onto a serving plate. Slide the omelet over the rice to cover it completely.

To serve, garnish with ketchup on the eggs or serve it on the side.