Use a sharp vegetable peeler and with a gentle, back and forth sawing motion, peel the tomato skin. Tip: the sawing motion should be very slight, just a quick back and forth motion moving along tomato. Cut the tomatoes in half and use your finger to flick out the seeds. Heat 2 tablespoons olive oil in a wide pan over medium-high heat until quite hot. Add the fresh and canned tomatoes, red pepper flakes, and season lightly with the salt and pepper. (I always start with a light hand with the salt and pepper because as the tomatoes reduce, the salt will become concentrated.) Cook tomatoes for a few minutes so soften.Crush tomatoes in the pan using a potato masher. Continue cooking until tomatoes are tender and sauce has thickened, 20 to 25 minutes. Taste and season lightly with salt again, keeping in mind the pasta will be plenty salty. If the sauce is too tart because your fresh tomatoes were not super ripe, add a 1/2 teaspoon of sugar.(You can make the sauce, which yields about 2-3 cups, ahead of time. Refrigerate it for up to two days or freeze it for longer storage.)
While the tomatoes are cooking, make the basil-garlic oil. Heat a small saucepan over low heat with 1/4 cup olive oil, garlic cloves, basil leaves and pepper flakes until the garlic is lightly browned. Keep the heat on low to allow the ingredients to warm slowly and release their flavors. Turn heat off and let cool for 10 minutes. The longer you let the oil sit, the more infused the oil. Strain the oil, discarding the solids.
To cook the spaghetti, bring a large pot of amply salted water to a boil. Cook spaghetti until just shy of al dente and drain, reserving a little of the pasta cooking water.
Add the cooked pasta to the sauce and cook over medium-high heat, gently tossing the pasta and the sauce together using a pair of wooden spoons and a lot of exaggerated movement (you can even shake the pan) until the pasta is just tender and the sauce, if any oil had separated from it, looks cohesive. (If the sauce seems too thick, add a little pasta cooking liquid to adjust it.)
Remove pan from the heat and toss the butter, basil and cheese with the pasta in the same manner (the pasta should take on an orange hue). Drizzle with just a bit of the basil-garlic oil on each plate (you might not use all of it).