Prepare the tomatoes: Pour the canned whole tomatoes and their juices into a bowl. Crush them by hand for a rustic texture, or pulse briefly in a food processor for a smoother sauce. Sauté the garlic: In a medium saucepan or skillet, heat the extra virgin olive oil over medium-low heat. Add the garlic and cook for about 30-60 seconds until fragrant, being careful not to let it brown or burn, which can make it bitter.
Simmer the sauce: Add the crushed tomatoes and their juices to the pan. Season with salt and stir to combine. Bring the sauce to a gentle simmer, then reduce the heat to low.
Cook down: Let the sauce simmer, uncovered, for 20 to 40 minutes, stirring occasionally, until it has thickened and the flavors have melded.
Finish with basil: Remove the pan from the heat. Stir in the fresh, torn basil leaves. If you used whole garlic cloves, remove and discard them at this point.
Adjust seasoning: Taste the sauce and add more salt if needed.
The sauce is ready to be used immediately with pasta, as a pizza sauce, or stored for later use.