To make the pumpkin purée, combine all ingredients in a small saucepan and bring to a simmer on medium heat. Simmer for about 5 minutes until the sugar is dissolved. Set aside to cool.

In a cocktail shaker filled with ice, add all martini ingredients and shake until combined and chilled. Pour into a martini glass. Optional: top with whipped cream and a sprinkle of pumpkin pie spice.