In a heavy bottomed medium saucepan, gradually whisk one cup of the milk into the corn starch until dissolved. Whisk in the remaining milk, cream and sugar. Cook over medium low heat, stirring constantly, until the mixture is simmering and slightly thickened, about 8 to 10 minutes. Transfer to a medium bowl set in a larger bowl of iced water. Stir in the vanilla, pumpkin, brown sugar and spice.

Let sit, stirring frequently, until completely chilled. Pour the mixture into the container of an ice cream maker and freeze according to the manufacturer’s instructions. Transfer the frozen ice cream to a large, airtight container. Cover and freeze until firm and set, about 4 hours. Serve frozen.