Cut off the end of the cucumber, and rub the cut surfaces together for about 10 seconds and rinse.
Slice the cucumber and cut into thin strips.
Cut 2 slices of cooked ham into thin strips.
Crack 1 egg into a bowl and beat well.
Heat a frying pan with medium heat and add 1 tbsp of vegetable oil. Then add the beaten egg and spread thinly over the pan.
Make a very thin omelet (usuyaki tamago in Japanese). When the surface is almost cooked, flip it over and cook for 1 more minute on very low heat, and then transfer to a cutting board.
For the soy-sauce based sauce, mix 1/4 cup each of lemon juice and mentsuyu (Japanese noodle soup base).
For the sesame seed sauce, combine 2 tsp of sesame oil, 2 tbsp of ground white sesame seeds (surigome), 1 tbsp each of soy sauce, Japanese rice vinegar, and sugar, plus 2 tbsp of tahini, and mix all together well.
Once cooled, cut the omelet into thin strips.
Boil 1 bunch of Chukamen noodles for 4 minutes (or follow the package instructions), taking care to separate the noodles with chopsticks.
Once they are cooked, drain and rinse the noodles well under cold water.
Arrange the noodles nicely on a plate, and then pour the sauce of your choice over the noodles.
Carefully arrange the 3 toppings on top of the noodles. It's ready! We hope you enjoy your "TOKYO FLAVORS, NEW YORK STYLE" meal! Itadakimasu!