This simple, addictive pasta is made up of two parts: 1) tomatoes that have been peeled, seeded, and then mashed as they bubble gently on the stove 2) garlic- and basil-infused olive oil that gets drizzled on just before serving. When making this pasta when tomatoes are no longer in season, I take a page from Jaden Hair of Steamy Kitchen and substitute one 12-ounce can of San Marzano tomatoes plus four fresh plum tomatoes (peeled and seeded) in place of the fresh ones. Using canned also has the upside of cutting down significantly on labor.
Peel the tomatoes by plunging them into boiling water for 10 to 15 seconds. Use a slotted spoon to lift them from the water and immerse them into a large bowl of ice water. Slip the skins off the tomatoes with the aid of a paring knife, if needed. Trim out the little bit of core and cut the tomatoes in half. Use your fingers to scoop out the seeds. Put the tomatoes in a bowl to catch all the juices.
Heat 2 tablespoons of the olive oil in your biggest sauté pan over medium-high heat. Add tomatoes with their juices and a pinch of crushed red pepper. Season lightly with salt and pepper. Cook for a couple of minutes, and then use a potato masher to break them up. Do this periodically as they cook until the tomatoes are tender, and the liquid reduced, about 20 to 25 minutes. This can be made ahead of time and stored in the refrigerator.
While the tomatoes cook, make the garlic basil oil. In a saucepan, combine the remaining ¼ cup of olive oil, garlic, 1 sprig of basil, and a generous pinch of crushed red pepper. Cook over low heat for 15 minutes to infuse the oil with flavor. Remove from heat and allow it steep until just before serving. Then, drain the oil through a sieve or fine strainer into a small bowl.
To finish the dish, bring a large, generously salted pot of water to a boil over high heat. Cook the spaghetti until al dente, scooping out about 1/2 cup of pasta water before draining.
Add the spaghetti to the pan of tomatoes. Add the chopped basil, butter, and Parmesan cheese. Gently toss until the pasta is evenly coated with the sauce. If the pasta looks like it could use a little moisture, add pasta water, a tablespoon at time, until nicely sauced. Taste, and add more salt and/or pepper if needed.
To serve, portion the pasta into serving bowls and drizzle a couple of teaspoons of garlic basil oil over each bowl. Pass more Parmesan with a grater at the table.