Rinse tomatoes well with cold water. Quarter tomatoes, removing and discarding the cores.
Place tomatoes in a large saucepan over medium-high heat; bring to a simmer. Cook 10 to 15 minutes or until tomatoes are softened, stirring occasionally. Remove pan from heat.
Line a colander with cheesecloth or a single layer of paper towels; strain tomatoes. Pass tomatoes through a food mill fitted with a fine disk and set over a bowl, or run them through a food processor fitted with a grating disk. Return tomato puree to pan over medium-high heat; bring to a vigorous simmer. Cook 20 minutes or until sauce reaches desired consistency. Stir in salt. Remove from heat.
Place basil sprig in a clean 16-ounce glass jar. Add sauce to fill jar; seal and store in refrigerator up to 1 week.