Bring 3 quarts of water to a boil and cook the udon about 6 minutes, or until tender but not mushy. If the starch from the noodles looks like it is about to boil over, lower the heat slightly. Drain the udon in a colander, rinse under cold running water, drain again, and set aside.
In the same, pot bring the 6 cups water, the tamari, and ginger to a boil. Lower the heat and simmer the broth simmer 10 minutes. Remove ginger with slotted spoon. Stir in the tofu and half of the scallions and cook 1 minute, or just to heat through. Place the miso in a bowl, then remove about 1/2 cup of the broth and stir it into the miso to dilute it and prevent lumping. Pour the mixture into the broth. Remove the pot from the heat so the miso doesn't boil. Stir in the sesame oil. Place the udon in large soup bowls and ladle some of the very hot soup over it. Garnish with the remaining scallions.
White miso is a sweet, mellowtasting variety that is actually yellowish tan in color. Miso can be purchased in natural foods stores.