Mix together all of the ingredients in a bowl until combined. Cover and refrigerate until use.

In a medium-sized bowl, whisk together the soy sauce, olive oil, steak sauce, mustard, smoked paprika, garlic powder, thyme, coriander, and black pepper until combined. Set side.

Cut the slab of tofu into thin slices, about 2-3mm thick (roughly the same thickness as gyro meat). Lay the slices to cover the bottom of a wide tupperware container, and generously brush them with the marinade, then continue with another layer of the slices and repeat until all the slices are in the container and have been brushed with marinade. Pour the remaining marinade over the top of the slices. Cover and refrigerate for 4 hours or overnight for maximum flavor.

Preheat your oven to 400°Fahrenheit. Line a lipped baking sheet with parchment paper and lay the tofu slices on the sheet, leaving at least 1 cm of space around each slice so the edges are not touching (this will make sure the edges get crispy). You may need multiple baking sheets depending on the size of your baking sheets and your oven. Give them another brush with the marinade. Place them in the oven and roast until the edges are golden brown and crispy, about 20 to 30 minutes depending on how thinly you sliced the tofu. (The thinner you sliced the tofu, the shorter the cooking time will be. Keep a close eye on them since you don't want them to burn.)

Meanwhile, heat the sauerkraut in a frying pan over medium heat until it's released some of its water, is sizzling, and is very hot. Using a wooden spoon or metal spatula, separate the sauerkraut into two disc shapes in the pan. Place a slice of the vegan cheese on each pile, cover the pan, and reduce heat to medium low. Allow to cook + steam until the cheese has melted, about 3 to 5 minutes.

Spread 2 tablespoons of the russian dressing on 1 side of toasted bread, and repeat with the remaining 3 slices of bread (you can refrigerate any excess russian dressing and enjoy for another use). Use a metal spatula to scrape 1 pile of the sauerkraut and cheese off the pan and place it on one of the dressing-ed sides of bread. Repeat with the other pile of sauerkraut and cheese.

Place your desired number of baked tofu slices on top of the cheese/sauerkraut, and then place the other toasted rye bread on top, dressing-side-down. Repeat with the other sandwich, and enjoy!