Preheat broiler and oven to 400ºF.
On a baking sheet, toss together tomatoes, 1 tablespoon EVOO, salt and ground black pepper. Roast in oven until golden brown and burst, about 10-15 minutes.
On a baking sheet, lay the bread halves cut side up. Drizzle with 1 tablespoon EVOO and place under broiler until golden brown, about 3-5 minutes. Remove and rub with garlic clove. Top the toast with burst tomatoes, Parmigiano Reggiano and shredded cheese. Place back under the broiler until melted, about 3 minutes.