This is a wonderful coconut-based ice cream! I usually use half light coconut milk and half full-fat coconut milk, but you could use all of either one or the other, depending on how health-conscious you are.
Mix 1/4 cup of the coconut milk with the 2 tablespoons of cornstarch and set aside.
Cut and puree the mangoes.
Combine the pureed mango, remaining coconut milk, sugar, and lime together in a saucepan and bring to a boil. When the mixture has just started to boil, take off the heat and immediately stir in the corn starch/arrowroot slurry. This should immediately cause the liquid to thicken (not a lot, but a noticeable amount; it will be thicker when it cools).
Set the ice cream mixture aside to cool. Freeze overnight.