In a bowl or large measuring cup, whisk together coconut milk until smooth. Transfer 1 cup coconut milk to a large bowl with a mesh strainer set on top. Set aside. 

Add remaining coconut milk to a medium saucepan with maple syrup, brown sugar, salt, spices and vanilla. Whisk until sugar is dissolved. Cook over medium heat until steaming. In a medium bowl, continuously whisk egg yolks while slowly drizzling 1 cup warm coconut milk mixture into yolks. Transfer egg mixture to saucepan, whisking to combine. Cook until mixture coats the back of a wooden spoon or rubber spatula. Pour through mesh strainer into reserved coconut milk. Add pumpkin puree to bowl, whisking until smooth. Cool over an ice bath to room temperature. Cover and chill thoroughly, roughly 4-6 hours or overnight. 

Churn according to manufacturer's directions. Transfer to a freezer safe container. Freeze until solid. 

Serve with optional caramel sauce or whipped cream.