1. Bring a large pot of water to boil for your pasta. Add salt to it.
2. Put the 3 Tbsp olive oil in a large skillet over medium-high heat. Add the onion and garlic when the oil is hot. Cook, stirring occasionally, until soft, 2 to 3 minutes.
3. Add the tomatoes and sprinkle with salt and pepper. Stir.
4. Cook the tomato mixture over medium low heat, or a heat setting where the sauce is bubbly but not boiling. Cook, stir occasionally until the tomato mixture breaks down and thickens up, 10 to 15 minutes. Taste the sauce and add more seasoning if needed.
5. Cook the pasta while the sauce is cooking. When the pasta is done, scoop out about a cup of cooking water and then drain the pasta.
6. Add a splash of the cooking water, a little drizzle of olive oil and the cooked pasta to the sauce and stir. You want the sauce to have a creamy texture, so add more cooking water if necessary. Taste and add more seasoning if needed.
7. Add the Parmesan cheese and basil and toss. Serve the dish with more cheese at the table if you'd like.
8. Serve, eat and enjoy!