In a large saucepan, combine the blueberries, sugar and water. Bring to a boil. Reduce heat; simmer, uncovered, until sugar is dissolved and berries are softened. Press mixture through a fine-mesh strainer into a bowl; discard pulp. Stir in cream. Cover and refrigerate overnight., Fill cylinder of ice cream freezer two-thirds full; freeze according to the manufacturer’s directions. (Refrigerate any remaining mixture until ready to freeze.) Transfer ice cream to freezer containers, allowing headspace for expansion. Freeze until firm, 2-4 hours. Repeat with any remaining ice cream mixture.