- Preheat the grill, setting the burners on high. Oil the grate.
- Slice the block of tofu into two rectangles lengthwise. Slice each rectangle into 12 square slices.
- Stack three slices of tofu, inserting two slices of cheese in between. Insert two toothpicks at a slight angle to hold them together. Oil lightly. Repeat with the remaining slices. Season with salt and pepper.
- Grill the tofu blocks for about 2 minutes on each side or until the cheese melts and begins to flow. Set aside on a warm plate. Remove the toothpicks.
- Toast the buns. Spread the inside with mayonnaise and mustard. Place the tofu cakes on the bottom buns. Top with arugula. Cover with the top buns.