'A pezzetti' means 'in pieces' in Italian. This recipe is courtesy of Maria D Ugo; like most Italian nonnas, she does not add lemon juice to the jars before sealing.
Prepare a large ice bath; set aside. Bring a large stockpot of water to a boil. Score an X in the bottom of each tomato. Working in batches, place tomatoes in boiling water a few minutes, just until skins start splitting. Using a large sieve, transfer to ice bath; let cool slightly. Transfer to a paper-towel-lined baking sheet.
Peel tomatoes, reserving skins and seeds in a large bowl; set aside. Using a sharp paring knife, remove stem from peeled tomatoes, and discard. Slice tomatoes in half crosswise, and scrape the seeds into the bowl with the peels. Cut tomatoes into 1/2- to 1-inch pieces, and place in a separate bowl. Pass the peels and seeds through a food mill on the finest holes, and add to tomato pieces. Season with salt; gently stir to combine.
Place a large basil leaf in the bottom of each pint or quart jar; fill with tomato mixture. Clean and dry top rim of each jar with a kitchen towel, and place lids and rings on the jars; twist tightly to seal.
Fill a large canning pot lined with a wire rack with water, and bring to a boil over high heat. (If you donâ??t have a canning pot, you can fit a large stockpot with a wire rack or with a layer of extra ring lids to keep the jars from sitting directly over the heat. The stockpot should be deep enough that the jars will be covered with water when they are added.)
When the water has come to a full boil, carefully place the jars in the water with tongs or a jar clamp. Boil pint jars 30 minutes and quart jars 45 minutes.
Carefully transfer jars to a baking sheet; let cool. When completely cool, check the lids to make sure they are sealed by pressing down on the middle. If the lid pops back, it is not sealed; refrigerate unsealed jars immediately, and use within 2 weeks. Sealed jars can be stored in a cool, dark place 2 years or longer.