Boil the udon noodles in boiling water and rinse under cold water.
Thinly slice the cucumber, carrot, and red onion.
Place the cooked udon noodles and vegetables in a bowl.
Mix the sauce ingredients (soy sauce, vinegar, sugar, sesame oil, mustard, etc.) together.
Add the sauce to the noodles and vegetables and mix well.
Transfer to a serving dish and sprinkle with sesame seeds to finish.