Place the nagaimo in a plastic bag and crush it with a rolling pin until finely mashed. Thinly slice the shiso leaves.

In a bowl, mix the mentsuyu and water. Chill the mixture in the refrigerator.

Heat sesame oil in a frying pan over medium heat. Add the beef and stir-fry until the color changes. Add mirin and soy sauce, and stir to combine.

Boil water in a pot and cook the udon noodles according to the package instructions. Rinse under cold water and drain well.