Add the cognac, butternut puree, Simple Syrup, Cointreau and lime juice to a cocktail shaker, add ice and shake vigorously. Double-strain into a glass over fresh ice.
Garnish with nutmeg and serve in a martini glass.
Combine the sugar and 1 cup water in a small saucepan and bring to a boil. Cook, stirring, until the sugar dissolves. Remove from the heat and let cool completely. Keep covered in the refrigerator up to 1 month.