In a Dutch oven, combine coconut cream, coconut milk, and ube halaya, whisking until the mixture is very smooth.
Optional: If mixture is not smooth, process in a blender and then strain through a fine mesh strainer. Note: I did not find that this step was necessary using homemade ube halaya.
Mix in half & half until well combined. Add sugar, corn syrup and salt, mixing well again and then bring to a simmer over medium low heat. Simmer until sugar is dissolved.
Remove from heat and cool to room temperature. Add ube extract and vodka, mix until fully combined. Refrigerate ice cream base overnight.
Churn ice cream in an ice cream maker according to manufacturer's directions. Transfer to an air tight container and freeze until ice cream is firm enough to scoop. Makes approximately 2 quarts.