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Preheat the oven to 400°F with a rack in the center position.
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Slice the ciabatta loaves in half horizontally. Place them cut-side up on a parchment-lined baking sheet.
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To make the sauce: In a large skillet, combine all the sauce ingredients. Cook over medium-high heat, stirring frequently, for 5 to 7 minutes, or until most of the tomatoes have split open. Then use the flat side of a flexible spatula to gently press the tomatoes against the bottom of the pan to release their juices. Once all the tomatoes are mashed, stir to ensure all the ingredients are well combined but still quite chunky. Remove the sauce from the heat to cool slightly while you prepare the other ingredients.
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To prepare the topping: Add the garlic, melted butter, oil, and salt to the bowl of a food processor. Process until the garlic cloves are coarsely minced and the mixture is homogeneous. (If you don’t have a food processor, mince the garlic with a knife and then combine it with the butter, oil, and salt in a bowl using a whisk.)
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Brush about 1/4 cup (roughly 50g) of the garlic mixture onto each sliced bread. Then spread about 3/4 cup (roughly 96g) of the sauce on each bread, followed by 1/4 cup (about 25g) Parmesan on each. Finish the garlic bread pizzas by adding 4 ounces (113g) mozzarella to each; tear the slices into smaller pieces as needed to fill any large gaps. It’s OK, and even desirable, for some of the tomatoes to peek through.
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Bake the garlic bread pizzas for 16 to 20 minutes, or until the mozzarella cheese is evenly melted and turns light brown in spots.
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Sprinkle the garlic bread pizzas with the fresh herbs and allow them to cool for 5 minutes before slicing and serving.
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Store leftover garlic bread pizza, well wrapped at room temperature for up to a day.