Make the pineapple syrup:
In a blender combine pineapple chunks, water, and sugar. Puree until smooth. Transfer to a small saucepan and over medium high heat bring to a boil. Reduce the heat to low and allow the mixture to simmer until it has a syrupy feel to it, about 10 minutes. Skim the foam that has accumulated on top and set aside to cool completely.
Make the infused vodka:
Add the pineapple to a blender and pulse a few times to break down the chunks and crush the pineapple. Doesn’t have to be perfect, but make sure it’s not pureed. We need some pineapple pieces. To a ½ gallon mason jar add the crushed pineapple, pineapple syrup, and vodka. Seal the jar and give it a vigorous shake to combine.
Place in a dark place and give it a shake once a day for at least a week and as long as 3 weeks. The longer you leave it, the more infused the pineapple will become.
When your vodka is nice and infused, line a strainer with cheesecloth over a measuring cup with a lip and strain the pineapple pieces. Wrap the pineapple pieces in the cheesecloth and give it a few healthy squeezes. Pineapple holds A.LOT. of vodka and we want it all. Transfer the infused vodka to a mason jar and seal with a tight fitting lid and store in the refrigerator.
Makes about 1.5 quarts of infused vodka.