Press the tomato halves and parmesan into each flatbread until half submerged. The tomatoes look best when facing cut side up. You can either press the basil leaves into the flatbread at this point and brush the extra virgin olive oil on top or you can put the basil in a food processor or blender with the extra virgin olive oil, and blend until just spreadable but not runny. If using the basil oil, brush it over the flatbreads when they come out of the oven.
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