Savory Korean Rolled Omelet with Vegetables and Seaweed

In a medium bowl, whisk the eggs until well combined. Add the finely diced carrot, chopped green onions, salt, pepper, and water (or milk). Mix everything well.

Heat a non-stick rectangular or round pan (about 20-24 cm / 8-9.5 inch diameter) over low-medium heat. Lightly coat the pan with about 1/2 tablespoon of vegetable oil.

Pour about 1/4 to 1/3 of the egg mixture into the hot pan, tilting to create a thin, even layer. Let it cook until the bottom is set but the top is still slightly moist.

Carefully place crumbled seaweed over about two-thirds of the cooked egg layer. Using a spatula, gently roll the cooked egg from one side (the side without seaweed) towards the other, forming a log. Push the rolled omelet to one side of the pan.

Lightly re-oil the empty part of the pan if needed. Pour another 1/4 to 1/3 of the egg mixture into the pan, making sure some of it flows underneath the already rolled omelet. Cook until this new layer is mostly set but still slightly moist on top.

Roll the existing omelet log over the new layer of egg, continuing to form a thicker roll. Push the growing omelet to one side again.

Repeat the previous two steps with the remaining egg mixture until all the egg is used and you have a thick, multi-layered rolled omelet. Cook for another 1-2 minutes, gently pressing down on all sides to ensure it's cooked through.

Carefully slide the Gyeran-mari onto a cutting board. Let it rest for a minute or two, then slice into 1.5-2 cm (about 0.6-0.8 inch) thick pieces. Serve warm with rice and other Korean side dishes.