How to Make It
Pour water to a depth of 3 inches into 2 large stockpots. Divide tomatoes evenly between pots, and sprinkle 1/4 cup salt in each pot. Partially cover, and bring each pot to a boil over high. Boil, stirring occasionally, until tomatoes are very tender, 20 to 30 minutes. Remove from heat.
Meanwhile, line several large strainers (about six strainers) or large colander food pans with several layers of cheesecloth, and set them over appropriately sized bowls or pans. Remove tomatoes using a medium saucepan, and pour into prepared strainers. Let cool 30 minutes, stirring occasionally with a wooden spoon to press out as much water as possible.
While tomatoes cool, line bottom of a large, deep stockpot with folded clean kitchen towels or burlap, and place 6 preserving jars in pot. Add water to cover jars by 1 inch (filling jars with water to prevent flotation). Bring to a simmer over medium-high, keeping jars hot until ready to use.
Working in batches, process tomatoes using an electric sauce maker or tomato press strainer. Return pureed tomatoes to a medium stockpot, and bring to a simmer over medium-high. Stir in citric acid, and remove tomato passata from heat.
Place a kitchen towel on a work surface. Using a jar lifter, remove jars from pot, letting water drain back into pot, and place on towel. Working with 1 jar at a time, add 1 basil sprig to each jar. Ladle hot tomato passata into hot jar, using a jar funnel to keep jar rim clean and leaving 1/2 inch of headspace. Release air bubbles in filled jar by running a bubble remover or nonmetallic spatula between passata and sides of jar; repeat a few times. Wipe rim of jar with a clean kitchen towel or paper towel. Top with lid, and screw on jar band until tight. Repeat with remaining jars and passata.
Using a jar lifter, carefully lower filled jars into simmering water, and make sure jars are covered by 1 inch of water (add hot water if needed). Bring to a boil over high. Cover and boil 45 minutes Uncover and turn off heat. Let stand 5 minutes. Place a kitchen towel on a work surface. Using a jar lifter, carefully remove jars from pot and place on towel. Let stand, undisturbed, at least 12 and up to 24 hours. Check seals (lids should be curved inward), and label. Store in a cool, dark place up to 1 year.