Position an oven rack in the top position, 3 inches below the broiler. Preheat the broiler. Whisk together 1 tablespoon of the oil and the garlic in a small bowl. Brush the rounded side of the mushroom caps with the garlic oil and arrange on a rimmed baking sheet, gill-side down.
Stir together the breadcrumbs, oregano and remaining teaspoon oil in a second small bowl; set aside.
Broil the mushrooms until browned, about 2 minutes. Turn each cap over, sprinkle with 1/2 teaspoon salt and 1/4 teaspoon pepper and broil until just softened, about 1 minute. Top each with a tomato slice, sprinkle with 1/8 teaspoon salt and broil until the tomatoes are softened and just cooked through, about 2 minutes. Top with the mozzarella, sprinkle with the breadcrumb mixture and broil until the breadcrumbs are browned, the mozzarella is melted and the mushrooms are fully cooked, about 45 seconds. Transfer to a platter and serve warm.
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