Bring a pot of water to a boil. Cook the tomatoes in boiling water until the skin begins to split, about 1 minute. Immediately remove the tomatoes and plunge into ice water for several minutes to stop the cooking process. Remove the tomatoes from the ice water; remove and discard the tomato skins. Cut the tomatoes into chunks. Blend the tomatoes in a food processor until smooth.
Heat the oil in a saucepan over medium heat; warm the crushed garlic in the oil until fragrant, being careful not to brown, 1 to 2 minutes. Add the blended tomatoes and salt; bring the mixture to a simmer and cook until the sauce thickens, 10 to 15 minutes. Remove the sauce from the heat and stir the basil through the sauce. Allow the sauce to sit for a few minutes to allow the flavor from the basil to blend into the sauce.