1. Core tomatoes; coarsely chop.Working in batches, transfer to a food processor or food mill. Process to a rough puree.

2. Rinse two 24-inch square pieces of cheesecloth.Wring out cheesecloth; layer pieces in a large glass bowl. Pour puree into cheesecloth; gather up ends, and cinch with kitchen twine. Tie ends of cloth together to make a loop. Hang sack from a cupboard door, placing bowl directly underneath to collect juices.

3. Let drain at least 1 hour; liquid will be pale. Transfer it to a large glass measuring cup, and set aside.

4. Squeeze bundle over emptied bowl to extract remaining liquid; pour into another measuring cup. You should have about 4 cups dark-red tomato juice; if needed, add enough reserved pale liquid to make 4 cups. Pass juice through a fine sieve into a bowl. Discard pale liquid.

5. Place 1 cup tomato juice in a small bowl. Sprinkle gelatin over liquid; let soften, about 5 minutes. Transfer mixture to a medium saucepan; stir over very low heat until gelatin dissolves. Stir in some of the juice to lower the temperature of the gelatin mixture, then add remaining juice and salt.

6. Pour mixture into a 9-by-4 3/4-by-2 1/2-inch loaf pan. Cover with plastic wrap, and refrigerate until jelled, at least 1 hour. To unmold: Slide a knife around inside edge of pan.Wrap loaf pan in a hot towel, and invert onto a serving platter. Garnish with basil sprigs.