Prepare the Mushrooms: Cut off the mushroom stems so they are even with the caps; discard the stems. Gently rinse the caps and pat them completely dry with paper towels. If you prefer a less earthy flavor, use a spoon to gently scrape the dark gills from the undersides of the caps.
Make the Marinade: In a small bowl, whisk together the olive oil, red wine vinegar, minced garlic, black pepper, and salt.
Brush this mixture generously over both sides of the mushroom caps.
Grill to Perfection: Preheat your grill to medium heat.
Place the mushroom caps, stemmed side down, directly on the grill rack.
Grill for 10 to 12 minutes, turning once halfway through.
Brush occasionally with any remaining marinade. The mushrooms are done when they are tender and have nice grill marks.
Once cooked, remove from the grill and cut into 1⁄2-inch / 1. 25 cm slices.
Assemble the Sandwiches: Place one slice of mozzarella cheese on the bottom half of each toasted roll.
Layer with the warm grilled mushroom slices, a handful of arugula, and a few tomato slices.
Place the top half of the roll on top and serve immediately.