Cook the rice until soft but not mushy. Fluff the rice and transfer it to a large bowl. While the rice is still hot, mix in the salt, sugar and sesame oil. Set it aside to cool slightly. It is easier to roll Kimbap when the rice is still a bit warm.
Lightly stir fry the vegetables like carrot and bell pepper. You can use them raw as well. Make sure to drain the salted cucumber well to prevent soggy Kimbap. Salting the shredded vegetables is optional. I prefer not to salt as there’s usually enough salt in the cucumber, the omelette strips. The dip or sauce served with the Kimbap is also salted.
Get all the things needed for rolling the Kimbap together. A small bowl of water to dampen your fingers will prevent rice from sticking to them. Cover your rolling mat with a piece of plastic wrap.
Lay one sheet of seaweed on the rolling mat, rough side up. Put a couple of generous tablespoons of the cooked rice on the sheet. Dampen your fingers with water and spread the rice thinly and evenly across the sheet, leaving 1 1/2-inch of sheet uncovered at the top end. Ideally, the rice layer should be about two grains thick.
Start layering the fillings at about 1-inch from the base of the seaweed sheet. Begin with two strips of egg and one strip of Danmuji next to each other. Lay some of the cucumber on top of the egg. Then add the bell pepper and carrots next. Last add the coriander.
Lift the base of the seaweed and roll it over the filling, squeezing and pressing from the centre out to the edges. Keep the rolling tight. Continue rolling until all the rice is rolled. Then lightly moisten the uncovered edge of the seaweed sheet with a small brush or your finger so it feels sticky and moist. Continue rolling over the wet edge then press down gently to seal. Set aside. Repeat with remaining ingredients.
Brush the top of the rolls with a thin layer of sesame oil. Slice each Kimbap roll carefully with a sharp knife, into 10 pieces. Plate, sprinkle with sesame seeds and serve immediately.