Peel the tomatoes. Bring a large pot of water to a boil. Meanwhile, fill a large bowl with ice water. Using a paring knife, core each tomato and score a small X in the bottom. In batches, carefully add the tomatoes to the boiling water and leave in just until the skins begin to split, 15 to 30 seconds, then transfer to the ice bath. Peel the tomatoes and discard the skins.
Chop the tomatoes. Cut the tomatoes in half and squeeze out and discard the seeds. Coarsely chop.
Prep the onions and garlic. Peel and chop the onions, and peel and slice the garlic.
Cook the sauce. Heat the oil in 2 large pots (at least 9 quarts each) over medium heat. Divide the onions, garlic, 3 tablespoons salt, and 1 teaspoon pepper between the pots and cook, stirring occasionally, until the onions are tender, 10 to 12 minutes. Add the tomato paste and tomatoes and cook, stirring occasionally, until the sauce has thickened, about 1 hour. Remove the basil leaves from the stems and stir into the sauce. Use the sauce immediately or freeze it for up to 3 months.