Preheat the oven to 400 degrees F. Line a baking sheet with parchment paper.
Place the cubed squash on the baking sheet. Sprinkle with the sugar and the cinnamon. Roast for 25 to 30 minutes, until it's somewhat dried out but also tender. Remove the squash and let it cool.
Place the squash in a large container or mason jar. Pour the bourbon over top and cover the jar. Let it sit and infuse for a week or two. When ready to use, drain the bourbon through a fine mesh strainer (maybe even once or twice and package or use!
Fill a chilled glass with a ice. In a cocktail shaker, shake the bitters vermouth and butternut infused bourbon for 30 seconds. Pour over ice and add a cherries or two!