Make the soup. Put the soy milk in a bowl, add the mentsuyu and mix lightly. Chill in the refrigerator if possible.
Make the meat-miso. Heat sesame oil in a frying pan, add the garlic, ginger and leek and stir fry until fragrant.
Add the ground meat to the pan. Stir fry until the meat is cooked and changes color. Add the miso, sake and sugar and stir fry some more. Add the soy sauce to finish, and turn the heat off.
Cook the noodles following package directions. Rinse in cold water to chill them completely. Drain well and plate.
Add the soup to the plates, top with the meat-miso and toppings, and serve.
Use whatever toppings you like. My kids love broccoli so I always add that.