In a large bowl or measuring cup with a lip, crack and beat eggs. Then add very finely chopped ham, carrots, green onions, sesame oil and salt. Whisk everything together until well combined.
In a non-stick pan (approx. 10 inches wide) set on low-medium heat (level 3 on the dial), lightly grease the bottom of the pan with oil by spreading it with a paper towel or brush.
Once the pan is hot, whisk your egg batter again and pour just enough egg batter until a thin layer forms. Swirl the pan so the egg mixture evenly distributes across. If needed, gently evenly disperse filling ingredients with chopsticks.
Fry for 2-3 minutes until top of the egg is cooked around the edges and the center is slightly moist but not runny. To test this, tilt your pan and if the egg is not running off of it, it's time to roll.
With a spatula, loosen the edges and the bottom of the omelette, if possible.
With two spatulas, fold the omelette about 1 inch towards the middle and gently pressing down. Continue to fold and roll until you reach halfway and stop.
Carefully slide the rolled omelette back to the middle of your pan. Then pour a thin layer of egg mixture to cover the open space, aiming for the tail edge of the omelette so that new egg layer sticks to the former one. Do not fill the other side of the pan beyond the rolled part.
Allow that layer to fry for 2-3 minutes.
Repeat the above process until you have depleted your batter. Carefully turn the roll on its side to seal in the remaining edge.
Transfer to a cutting board to slice into 0.75-inch-thick pieces. Serve and enjoy!