To prepare marinade, combine first 6 ingredients in large shallow baking dish. Cut 2 slits into top of each eggplant slice. Add the eggplant slices, tofu slices, and mushrooms to marinade. Let mixture stand 6 minutes, turning after 3 minutes. Arrange eggplant, tofu, and mushrooms on a broiler pan coated with cooking spray. Broil 6 minutes on each side. Pour remaining marinade over eggplant, tofu, and mushrooms.
Combine mayonnaise and horseradish in a small bowl. Spread mayonnaise mixture evenly over muffin halves. Top bottom half of each muffin with 1 eggplant slice, 1 tofu slice, 1 mushroom, remaining eggplant slice, and muffin top.