Rinse shitake mushrooms and soak in hot water until soften, about 20 minutes. Remove stems and slice caps thinly. Reserve soaking liquid.
In a medium sized pot, combine white rice, brown rice, and buckwheat groats. Rinse and drain until water runs clear, about 4 to 5 times.
Combine water with reserved mushroom soaking liquid to make a total of 5 cups (1.2 liters). Pour into pot with mixed grains and dashi. Bring to a boil. Add mushrooms, soy sauce, and mirin. Reduce heat and simmer for 15 minutes.
Add sliced tofu and salt (if needed) and continue to simmer for another 5 minutes. If porridge appears to be a little too thick, add some water to bring to desired consistency.
Beat eggs lightly in a small bowl. Pour into the porridge and swirl with a fork. Turn off stove.
Serve in bowls topped with sliced green onions, umeboshi, toasted sesame seeds, and sichimi togarashi.