Prepare the tomatoes. Wash under cold running water, pat dry, and remove the stems. Cut in half lengthwise, then scoop out seeds and goop with a spoon to discard.
Take each tomato half and carefully run the cut side over a grater with large holes placed over a large bowl. I like to use a box grater. Grate the tomato so that all of the flesh falls into the bowl and you are left with just the skin. Discard the skin. Repeat with the remaining tomato halves.
In a stainless steel saucepan, warm the olive oil over medium heat. Add the onion and cook for about 5 minutes until slightly softened, stirring occasionally.
Stir in the garlic and salt. Cook for another minute until fragrant.
Add the bowl of tomato pulp and juices to the pot, followed by the basil leaves.
Cook, over medium-low or low heat to maintain a simmer with gentle bubbles, for 30 to 60 minutes or until the juices have thickened into a sauce-like consistency. Stir occasionally and adjust the heat as needed to maintain a simmer.
Once the sauce has thickened, remove from heat. Stir in the red wine vinegar.
Use a hand blender to puree all or some of it, depending on your desired texture. Alternatively, you can transfer the sauce to an upright blender or food processor to puree. Leave the lid slightly cracked or remove the plastic circle in the center of the lid to allow steam to escape (and do not overfill).
Serve over pasta of choice. I recommend spaghetti! Enjoy!
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