Fill a large pot with water and bring to a boil. Place the tomatoes in the boiling water for about 30 seconds, then transfer them to a large bowl of ice water. (You may need to do this in 2 batches.)
Remove the skin from the tomatoes. Cut off the cores and remove the seeds. You can do this by scraping the seeds out with your finger, and it’s okay if you don’t get them all. (I use food-prep gloves to protect my sensitive hands.)
In a large pot, cook the garlic in the olive oil over low heat for a few minutes.
Add the remaining ingredients and simmer over medium low heat for about 2 hours, or until it reaches the consistency you like. You can turn the heat up a bit if you don’t have 2 hours.
Remove the basil stalks and leaves, and serve warm.