Step 1

In a large ziptop bag, combine the soy sauce, balsamic vinegar, oil, garlic, Italian seasoning, and black pepper. Add the mushroom caps and seal the bag, removing as much air as possible. Gently swish the marinade around the mushrooms, then place the bag in a shallow dish. Allow the mushrooms to sit at room temperature for at least 30 minutes while you prepare any desired toppings, or refrigerate for up to 1 hour. Turn the bag once or twice while the mushrooms sit so that they are coated evenly.

Step 2

Heat an outdoor grill or indoor grill pan to medium heat. Once hot, brush the grate lightly with oil to prevent sticking. or lightly spray the grill pan with nonstick spray.

Step 3

Remove the mushrooms from the marinade, shaking off any excess. Reserve the marinade in the bag for basting. Grill the mushrooms on both sides until tender, about 10 minutes total, brushing them with the marinade several times throughout.

Step 4

When the mushrooms are in their final minute of cooking, turn two of them so that their undersides (the ones that previously had the gills and stem) are facing up. Top each with 1 slice of cheese, then stack a second mushroom on top, gill-side down, so that the cheese is in the middle. Place a second slice of cheese on top. Reduce the heat to low and cook just until the cheese is melted.

Step 5

During the last few minutes of cooking, if desired, grill sliced onions and toast the buns. To assemble, spread a thin layer of pesto on the cut sides of each bun. Place the arugula on the bottom bun, then top with a grilled portobello mushroom stack, onion, and tomato. Add the top bun. Enjoy immediately.