1. Make the Butternut Squash Syrup: In a large saucepan, combine the squash, sugar, 2 cups water, the cinnamon, cloves, allspice and nutmeg. Bring to a boil, then reduce the heat and simmer until the squash is soft, about 15 minutes. Strain the mixture through a fine-mesh sieve, reserving the syrup. Pick out the cinnamon, cloves and allspice, and discard. Transfer the squash and the syrup to a blender. Add remaining 1 cup water and purée until smooth. Strain the purée through a fine-mesh sieve, let cool and transfer to an airtight container. Refrigerate until using.

2. In a cocktail shaker, combine the rums, curaçao, milk, bitters, ginger juice and 1 ounce of the Butternut Squash Syrup. Fill with ice and shake until chilled. Strain into a coupe and garnish with the rosemary sprig. Serve.