Press the tofu:

Place between a couple sheets of paper towels on a plate. Place the tofu on the paper and then cover with another couple sheets of paper towels (you can also do this with a clean kitchen towel) and place another plate on top of the tofu. Put a couple cans on the plate to add some weight to help remove water from the tofu. You can let the tofu sit for 15 minutes and continue with the recipe.

Sauté the vegetables:

Heat a large pan over medium high heat for several minutes. Add 2 tablespoons of oil and the mushrooms. Lightly season with salt. Let the mushrooms sit for 1 minute untouched, then flip them over and cook for another minute untouched. Sauté for another couple minutes until cooked. (This will help the mushrooms brown instead of steam). Transfer to a colander sitting in a bowl.

Return the pan to the stove and add 1 Tablespoon oil and the onions. Season lightly with a couple dashes of salt and ground black pepper. Sauté for a couple minutes and then lower the heat to medium and continue cooking for 8-10 minutes, stirring regularly, until the onions are soft, translucent, and starting to brown. Add the garlic and cook for another minute. Take the pan off of the heat and set a colander in the sink. Add the onions to the mushrooms in the colander to drain off any liquid.

Make the patty mixture:

Place the onion and mushrooms into the food processor along with the pressed tofu. Pulse 3-4 times until you have a roughly chopped mixture. Transfer this mixture into a large bowl and add the scallions, panko breadcrumbs, soy sauce, oyster sauce, eggs, and ground black pepper. Use your clean hands and mix well.

Use a 1 cup scoop (you can also eye ball) and portion out the mixture into 6 balls.

Shape the balls to form thick patties.

Make the sauce:

Combine the sake, mirin, worcestershire sauce, oyster sauce, soy sauce, cornstarch, water, and a couple dashes of ground white pepper in a small saucepan. Mix well. Bring to a simmer over medium heat, whisking to keep the sauce smooth. Once it thickens, give it another minute, and then turn off the heat and set it aside.

Cook the patties:

Right before cooking, sprinkle the top of each patty with a teaspoon of flour and smooth it over the surface of the patty. Heat a large non-stick skillet over medium heat for several minutes and add 2 tablespoons of oil. Swirl the oil to coat the pan. Add the patties, flour side down, to the pan in one layer (you can do this in batches if you cannot fit all of the patties in the pan). Cook the patties for 3 minutes. Then again coat the top of each patty with a teaspoon of flour and gently flip the patties over, cooking for another 3 minutes. Add another tablespoon or two of oil if the pan looks dry. Next, cover with a lid and continue cooking for another 2-3 minutes, until the center of the patties is hot (you can check with a skewer or tip of a knife).

Transfer the mushroom and tofu patties to the plate, pouring the sauce on top.