Preheat the oven to 425 degrees F. Line a baking sheet with foil.
Scrape out the gills of the mushrooms with a spoon, being careful not to break the cap. Rub the mushrooms with 2 tablespoons of the oil and half the garlic. Sprinkle with 1/2 teaspoon salt and 1/4 teaspoon oregano. Place the mushrooms, gill-side up, on the prepared baking sheet, and roast until tender, 15 to 25 minutes. (If the mushrooms are thicker than 1 inch, they will take longer to cook.)
Meanwhile, toss the bread pieces in a medium bowl with the remaining garlic, 1 tablespoon olive oil and 1/4 teaspoon oregano, 1/4 teaspoon salt and the red pepper flakes. Transfer them to a medium skillet over medium heat, and stir until they turn golden and crisp on the edges, 5 to 6 minutes. Return the croutons to the bowl.
While the mushrooms are still hot, pat them dry with a paper towel. Top each with 1 teaspoon tomato paste, spread evenly, and slices of mozzarella to cover. Divide the sun-dried tomatoes and croutons between the 4 mushrooms, and place in the oven to melt the cheese, 4 to 5 minutes. Sprinkle with basil leaves.
Cut each mushroom into 4 to 8 pieces, depending on the size of the mushroom.
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