Combine the yogurt, cream, sugar, pumpkin puree, brandy, vanilla extract, pumpkin pie spice, and salt in a mixing bowl. Whisk together until the sugar and salt have completely dissolved. Cover, and refrigerate overnight.
Pour the chilled mixture into an ice cream maker and freeze according to manufacturer's directions until it reaches "soft-serve" consistency, about 20 minutes. Transfer ice cream to a one- or two-quart lidded container. For best results, ice cream should ripen in the freezer for at least 2 hours or overnight.