In a mixing bowl, mix about 1/3 cup of miso paste into 2 cups of room temp water. (On average I used about 1/3 of what is recommended on the box of miso for 4 quarts.).
Wrap tofu in two layers of paper towels and weigh it down for 20 minutes; then diced into small cubes.
Heat the butter in a heavy 6 quart pan. When the butter has melted, add onions and garlic. Cook uncovered, over med heat for 10 to 15 minutes, stirring occasionally. Heat and stir onions until they turn transparent but not brown. Do not let them burn!
When onions are transparent add fresh mushrooms. Cook and stir for 3 minutes.
Pour water into the heavy 6 quart pan until it is half way full . Increase heat and bring to a simmer.
To the 6 quart pan add, tofu, (and mushrooms if you are using rehydrated shiitake) and cook for 10 minutes.
Turn down heat just below a simmer on the pan and add two cups of room temp water (new water not the miso yet). Also, add salad greens to the pan, cook, stirring occasionally, for 3 minutes.
Turn off heat.
Add 1/2 cup stock from the 6 quart pan to the mixing bowl with miso paste. Mix until smooth.
Add miso mix to the 6 quart pan. Stir.
Season with soy sauce, fish sauce, and rice vinegar.