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Prepare the pasta according to manufacturer's directions, being careful not to overcook. When pasta is done boiling, reserve some of the water for possible use in sauce.
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While the pasta is boiling, combine the cherry tomatoes, scallions, garlic, parmesan, basil, and olive oil in a food processor. Pulse the tomatoes until they are coarsely chopped, being careful not to puree. Set aside. Season the sauce with salt and pepper. This can also be done in a blender, but it's even more difficult to make sure the sauce doesn't puree in a blender. We want the sauce to be a bit chunky!
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When pasta is cooked, drain the pasta, put back in pan, and toss with the tomato mixture, adding the cheese cubes. (Add a bit of the water the pasta boiled in if the sauce seems a bit dry.) Serve immediately.