In a bowl, stir together 1⁄4 cup coconut milk and the cornstarch; set slurry aside. In a 4-qt. saucepan, whisk together remaining milk and the coconut cream, sugar, syrup, and salt; bring to a boil over medium-high heat. Cook for 4 minutes; stir in slurry. Return to a boil and cook, stirring, until thickened, about 2 minutes. Place cream cheese in a bowl and pour in 1⁄4 cup hot coconut milk mixture; whisk until smooth. Then whisk in remaining coconut milk mixture and the rum. Pour mixture into a plastic bag; seal, and submerge in a bowl of ice water until chilled or just chill it in the fridge over night. When ready to churn, toast your coconut in a large pan until golden brown and set aside to cool while you churn your ice cream until soft serve consistency. Now slowly add the cooled flakes to the still churning ice cream until incorporated.

Fill the ice cream into a container and put into the freezer until firm enough to form proper scoops.

Enjoy with plenty coconut flakes on top!