Cut The Tofu Into Slabs 1-inch thick-firm tofu often comes in pieces that size-and drain them: Set them on a bread board or the back of a baking sheet and raise 1 end; point the lower end toward the sink to let the water drain off. Cover the tofu with another tray and weigh it down with something heavy, such as a few cans of tomatoes. Let the tofu drain for about 1/2 hour. This will remove excess water and allow the marinade to penetrate without being diluted. While the tofu is draining, prepare the marinade. Simmer the mushrooms in the water for 15 minutes. Heat a small heavy skillet and toast the oregano or marjoram slowly until it is fragrant. Add the oregano and the remaining ingredients to the pot with the mushrooms. Bring to a boil, and simmer slowly a few minutes more. Remove the tofu from the draining board and arrange it in a single layer in a square or rectangular non-corrosive pan. Strain the marinade through a coffee filter or paper towel and pour it over the tofu. Cover with plastic or a lid and refrigerate at least 1 day, preferably longer.