In a small bowl, mix together 2 tablespoons of the coconut milk with the cornstarch and whisk until smooth. Set aside.
In a large saucepan (Jeni recommends a 4-quart), add coconut milk, sugar and corn syrup, whisking together. Bring to a rolling boil – for me, this was over medium heat. Keep a close eye on the mixture because if it gets too hot, it will boil up and over very quickly. You want it to the point when the milk is bubbling and rolling but now boiling over. Once it comes to that point, boil for 4 minutes. I stirred occasionally here. After 4 minutes, remove from heat and very slowly whisk in the cornstarch mixture. I did it in 3 parts – adding 1/3 of it and whisking at a time. Bring back over heat and bring to a rolling boil again, this time stirring with a spatula while the mixture just thickens slightly – about 1-2 minutes.
Grab another very large bowl and fill it halfway full with cold water, adding a bunch of ice cubes as well. Remove the coconut milk mixture from heat and pour the it into a one gallon freezer ziplock bag, pushing the air out and sealing it. Place it in the ice bath for 30-45 minutes until cold, adding more ice if needed. I actually set my bag right IN the ice bath, then carefully poured in the milk.
After 30 minutes or so, pour the ice cream mixture into your ice cream maker and churn according to the directions. When it begins churning, you can toast your marshmallows. If you have a gas stove you can do it that way, or you can place them under the broiler for a little less than a minute or until your desired doneness. You don't have to use the whole bag - use as many as you'd like. After 10-15 minutes of churning, add in the vanilla extract and spoonfuls of marshmallow fluff while still churning. (If you don't have an opening in your ice cream make to add, you can add the vanilla at the beginning and fold in the marshmallow at the end.) After 5 more minutes, add in the toasted marshmallows one at a time, making sure they get mixed in.
Once churned to your desired consistency, place in a freezer-safe container, add more marshmallows if desired, cover with a lid or layer of plastic wrap pressed on the ice cream, and freezer 2-6 hours.
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