Combine broth, blueberries and brown sugar in a medium non-reactive saucepan. Bring to a boil.
Reduce heat and simmer, uncovered, stirring and mashing blueberries occasionally, until mixture is reduced and coats a spoon, about 25 minutes. Mixture will be thin. Remove from heat.
Using a hand blender, purée until smooth. Stir in vinegar and salt. May be refrigerated for up to 3 days or frozen for up to 1 month.