Bring a large pot of water to a boil. Place a large bowl of ice water next to the stove. Using a sharp paring knife, core the tomatoes and score a small X into the flesh on the bottom.

Place the tomatoes in the boiling water, in batches, until the skins are slightly loosened, 30 seconds to 2 minutes.

Using a slotted spoon, transfer the tomatoes to the ice water and let sit in the water for 1 minute before removing.

Place a sieve over a bowl; working over it, peel the tomatoes using a paring knife, and let the skins fall into the sieve.

Halve the tomatoes crosswise and scoop out the seeds with a hooked finger, letting the sieve catch the seeds. Press on the seeds and skins to extract any extra juice. Coarsely chop the peeled tomatoes and set aside.

Heat oil in a Dutch oven over medium heat. Add garlic and cook, stirring constantly, until fragrant and just beginning to color, 2 to 3 minutes. Add onions and salt, stir to coat, cover and cook, stirring often and adjusting heat as necessary to prevent burning, until soft and turning golden, 10 to 15 minutes. Stir in tomato paste and oregano and cook, stirring often, until the tomato paste is beginning to brown on the bottom of the pan, 2 to 4 minutes.

Pour in wine and vinegar; bring to a simmer, scraping up any browned bits with a spoon. Cook until reduced slightly, about 2 minutes. Add the tomatoes and any juice; return to a simmer, stirring often. Reduce heat to maintain a gentle simmer and cook, stirring occasionally, until the tomatoes are mostly broken down, about 25 minutes.

Remove from the heat; stir in basil and pepper. Transfer the sauce, in batches, to a blender or food processor. (Use caution when pureeing hot liquids.) Process until desired consistency. For a smooth sauce, puree it all; for a chunky sauce, puree just half and mix it back into the rest of the sauce.

MAKE AHEAD TIP: Cover and refrigerate for up to 5 days or freeze for up to 6 months.