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1
Give blueberries a good rinse, then add to a large pot (no need to dry them). Warm blueberries over medium heat, stirring occasionally. Cook blueberries until they release a decent amount of liquid. You can eyeball this step. I stopped cooking the blueberries once more liquid was visible than solid berries. Cooking the berries this way speeds up infusing times. Remove from heat and let cool to room temperature.
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2
Add blueberries with juices to a large, airtight jar. Pour in vodka. Seal the jar and store in a cool, dark spot.
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3
Each day, give the jar a little shake, then taste the vodka. As the days go on, you'll notice that the blueberry flavor will get stronger. I was pleased with the flavor after 6 days of infusing; however, this can vary based on taste. Once you are satisfied with the blueberry flavor, stir in the basil leaves.
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4
Seal the jar once again and store in a cool, dark spot. After 24 hours, pour the mixture through a fine-mesh basket strainer into a clean bowl or jar. Discard the solids.
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5
The more solid matter that you strain from the vodka, the longer the alcohol will last. I find that I use up my infusions several weeks after making them, so I'm fine with a single strain. If you are planning on keeping this infusion for an extended period of time, line the strainer with several layers of cheesecloth, and strain again.