Combine first 6 ingredients in a medium saucepan. Bring to a boil, stirring until sugar dissolves.
Reduce heat to low and simmer 10 minutes. Discard rosemary.
Mix in cranberries and 3/4 cup sugar. Cook over medium heat until liquid is slightly reduced and berries burst, stirring occasionally, about 6 minutes. Cool. Transfer sauce to a bowl, chill until cold.
Can be prepared one week ahead, keep covered and refrigerate.
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