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.
Photograph by Andrew Purcell
Recipe courtesy Food Network Magazine