How to Make It
In a heavy medium saucepan, combine the coconut milk with 1 cup of the half-and-half and the salt and bring to a simmer. In a bowl, whisk the sugar with the egg yolks until thick and pale. Gradually add 1 cup of the coconut-milk mixture, whisking vigorously, then whisk in the remaining coconut-milk mixture in a steady stream. Pour the mixture back into the saucepan and cook over low heat, whisking constantly, until thickened, about 5 minutes; do not let the custard boil or the eggs will curdle.
In a bowl, stir the tapioca starch with the remaining 2 tablespoons of half-and-half until smooth, then whisk the mixture into the custard along with the dried coconut. Simmer until thick enough to coat the back of a spoon, about 2 minutes. Transfer the custard to a heatproof bowl and let cool to room temperature, then refrigerate until chilled.
Pour the custard into an ice cream maker and freeze according to the manufacturer's instructions. Add the chopped mint halfway through to ensure even distribution. Transfer the ice cream to an airtight container and freeze until ready to serve, for up to 2 days. Scoop the ice cream into bowls, garnish with mint leaves and serve.