1. Cut plums in half and remove pits. Cut halves into 1 1/2-inch pieces. Combine plums, 3/4 cup water, the sugar, and the salt in a 5-quart nonreactive saucepan. Cook over medium heat until plums break down, about 30 minutes. Stir occasionally to prevent plums from scorching.

2. Remove from heat and cool slightly. Puree mixture in a food processor and strain into a medium bowl set over an ice bath to chill. Stir in cognac and vinegar.

3. Freeze mixture in an ice-cream maker according to manufacturer's instructions.