Lay the tofu on a cutting board and slice each piece in half horizontally. Sprinkle the tofu pieces evenly on one side with the allspice and mustard powder. Heat 1/2 tablespoon butter in a large nonstick skillet over medium-high heat. Add the tofu and cook, turning once, until golden brown, about 1 minute per side. Wipe out the skillet and remove from the heat.
Spread each slice of bread with 1 tablespoon Russian dressing, then sandwich with the sauerkraut, tofu and cheese.
Heat 1 tablespoon butter in the skillet over medium heat. Add 2 sandwiches and cook, turning once, until the cheese melts and the bread is toasted, about 3 minutes per side. Repeat with the remaining butter and sandwiches.
Toss the mixed greens, cornichons, brine, mushrooms and olive oil. Serve the sandwiches with the salad.