Wash the blueberries and drain them well. Remove any bruised or damaged berries to ensure the best quality glaze.
In a medium saucepan, heat the olive oil over medium-low heat. Add the blueberries and begin to simmer gently.
Pour in the balsamic vinegar, orange juice, and water. Stir well to combine the flavors.
Add the brown sugar, rosemary sprig, and a pinch of salt. Continue to simmer over low heat until the blueberries soften and the glaze begins to thicken, about 15 minutes.
Remove the rosemary sprig. Use an immersion blender to purée the glaze until smooth. For an even smoother consistency, strain the glaze through a fine-mesh sieve.
Let the glaze cool slightly, then transfer it to a sterilized jar. Store in the refrigerator for up to a week.
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