Preheat oven to 400 degrees. Place mushrooms and garlic on a rimmed baking sheet; coat with oil and vinegar. Sprinkle with 1 teaspoon salt, and season with pepper. Roast, shaking sheet occasionally, for 20 minutes. Flip mushrooms and garlic to recoat with oil. Add tomatoes; flip to coat in oil, sprinkle with remaining teaspoon salt, and season with pepper. Roast until mushrooms are tender and tomatoes are soft, 20 minutes more.
Rub softened garlic onto mushrooms. Place 1 mushroom on each of 4 plates, and top each with some basil. Stack another mushroom and 1 mozzarella slice onto each. Layer more basil, 1 tomato slice, more basil, then another tomato onto each. Divide arugula among plates, and drizzle with pan juices. Serve with bread if desired.