Place blueberries, shallots, sugar, vinegar, ginger, lime juice, salt and pepper in a large saucepan over medium-high heat. Stir until the sugar dissolves, about 5 minutes. Bring to a simmer, reduce heat to medium-low and simmer, stirring occasionally, until the blueberries have mostly broken down and the sauce has thickened, 20 to 30 minutes. Spoon into glass jars or a large bowl and refrigerate until chilled and thickened, about 4 hours.
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