Add the olive oil and garlic to a large dutch oven. Turn heat to medium high and cook garlic, occasionally stirring, until fragrant and lightly golden, 1–3 minutes. Remove garlic from the pot and discard.

Carefully lower the chopped tomatoes into the hot oil. Stir constantly until the tomatoes let off some liquid and the sauce starts to bubble steadily. Season generously with salt. Lower heat to medium and simmer, stirring occasionally, for about 40 minutes, until the tomatoes break down and the sauce reduces significantly.

Set a metal sieve, strainer, or food mill over a medium bowl. Carefully pour in the tomato sauce. If using a sieve or strainer, push the sauce through with a flexible spatula until all that remains are seeds and skins. Be sure to repeatedly scrape off the valuable pulp collecting on the bottom of the sieve (by holding the sieve against the edge of the bowl and pulling it back). You should have about 4 cups of sauce in the bowl. Taste and add more salt if needed. If you are making it ahead of time, you can refrigerate. Then return the sauce to the dutch oven and continue to heat.

Meanwhile, cook the spaghetti in a large pot of salted boiling water for 6 minutes. It is important to not cook to doneness. Drain the pasta and add to the sauce.

Turn heat to high and cook, constantly stirring, until sauce reduces slightly and pasta is well coated but not drowned in the sauce, about 2 minutes. Remove the pot from the heat and let it sit uncovered so the pasta can absorb the sauce further, about 5 more minutes. Serve family style or as individual nests with fresh basil and grated Parmesan.