
Soften the garlic: In a large saucepan over medium-low heat, warm 1/4 cup oil with the garlic until it sizzles, about 2 minutes. Add a pinch of red pepper flakes and press the garlic to release its flavor, but don’t let it brown. For a milder flavor, discard the garlic and keep the infused oil. Leave it in for a bolder taste.
Add the tomatoes: Carefully pour in the can of tomatoes and their juice. Use a potato masher or sturdy wooden spoon to break up the tomatoes into large pieces. Season with 1/2 teaspoon of salt and raise the heat to medium-high. Bring to a boil, then lower the heat to maintain a very gentle simmer.
Simmer the sauce: Cover the pan partially and cook, stirring every now and then, until the tomatoes have darkened in color and the sauce has thickened, 35 to 40 minutes. The oil should be pooling on the surface. If the sauce thickens too much before it tastes sweeter and richer, add a splash of water.
Process the sauce: Turn off the heat and let the sauce sit for 10 minutes to cool, then strain through a fine mesh strainer set over a bowl (you can also use a food mill if you’d like). Press the tomatoes through the strainer to make a smooth sauce, then return the sauce to the pan. Taste and add another pinch of salt, if needed.
Season: Stir in the remaining 2 tablespoons of olive oil. Lay the branch of basil on top of the sauce and bring to a simmer over medium heat. Stir the sauce and cook gently for about 15 minutes. The basil will wilt into the sauce and infuse it with flavor. Turn off the heat and discard the branch of basil. Add a few more fresh basil leaves if you’d like. Cover the pan to keep the sauce warm.
Combine: Bring a large pot of water to a rolling boil and salt it generously. Drop in the pasta and cook according to the package instructions until just al dente. Use a pasta fork, tongs, or a skimmer to transfer the pasta directly to the pan with the sauce. Add a splash of the starchy pasta water and turn the heat under the pan on to low. Cook, tossing pasta and sauce together, for about 2 minutes, or until the noodles are cooked and well coated with the sauce.
Serve: Divide the pasta between bowls and spoon any remaining sauce on top. Sprinkle with Parmesan cheese (if using) and basil. Enjoy!