Preheat oven to 350 degrees F.

Peel butternut squash, cut in half lengthwise, then clean out seeds and guts. Discard skin, seeds and guts. Cut the squash up into 1.5-inch chunks. Spread out in an even layer on a parchment-lined baking sheet. Bake until just tender (test by inserting the tip of a knife), 20 – 30 minutes. Do not overcook here. The squash should be tender, but not falling apart. Let the squash cool to room temperature, then transfer to a large mason jar.

Add vodka to the jar until it covers the squash by 1 inch (I used between 750 ml and 1 L). Seal the jar and store in a cool, dark spot.

Give the jar a gentle shake every few days. Start tasting the vodka after 1 week. The finished infusion should taste very strongly of butternut squash. I was pleased with the flavor after 2 weeks; however, this can vary based on taste.

Once you are satisfied with the butternut squash flavor, pour the mixture through a medium-mesh basket strainer into a clean bowl or jar. Discard the solids. Strain again through a fine-mesh strainer into another clean bowl or jar. Set aside while you prepare the 5-Spice Syrup.

In small saucepan, combine sugars, spices and water. Bring mixture to a boil over medium-high heat, stirring to dissolve the sugar. Once the mixture comes to a boil, drop the heat to low, and simmer for 5 minutes. Let the mixture cool completely, then strain out all of the spices. Discard spices.

Pour syrup into the infused vodka, stirring to combine. Cover and let rest for 1 more day before serving.