Cook noodles per package instructions. Drain and transfer cooked noodles to a flat tray. Drizzle a small amount of sesame oil to the noodles and mix until evenly coated. Spread the noodles apart and set aside by the window or next to a fan to cool.
In a bowl, add sesame paste and hot water, mix until smooth. Then add soy sauce, vinegar, sugar, and minced garlic. Mix until well combined and set aside.
To make egg strips, whisk 3 eggs and a dash of salt in a bowl. In a pan or skillet, drizzle 1 tbsp of oil. Pour beaten eggs into the pan, flatten out and cook for about 30 seconds. Carefully flip over and cook the other side for about 30 seconds. Remove from the pan and slice into thin strips.
Assemble: Add cold noodles to a bowl and top with thinly sliced cucumber, carrots, egg strips, and shredded chicken. Drizzle with sesame sauce. Garnish with green onion and sesame seeds. Enjoy!
