In a large saucepan or deep skillet, warm the olive oil at low heat. Add the garlic and cook until golden, about 3 minutes. Stir in the basil.
Pour in the tomatoes with their juices, bring the sauce to a boil, and then add the Kosher salt. Reduce the heat to low and simmer 45 to 50 minutes. As the sauce thickens toward the end, stir in the balsamic vinegar. Remove the pan from heat.
*To store: cool the sauce to room temperature before storing. It will keep in a covered container in the refrigerator for up to 2 weeks, and it will keep in a covered freezer-safe container for up to 3 months.