Toast:

Combine in a medium saucepan and bring to a simmer over medium-low heat, stirring to dissolve the sugar:

Stir in 1 cup of the toasted coconut, remove from the heat, cover, and steep for 30 minutes.

Strain the milk through a fine-mesh sieve into a bowl, pressing firmly on the coconut to extract all the liquid; discard the coconut. Return to the saucepan and bring to a simmer over medium-low heat. Beat together in a medium heatproof bowl:

Slowly stir in about ½ cup of the milk mixture, then stir the egg mixture into the rest of the milk. Cook over low heat, stirring constantly, until the custard reaches 175°F and coats the back of a spoon. Do not allow the mixture to boil. Transfer to a bowl and refrigerate the ice cream base until cold, overnight if possible, or quick-chill in an ice water bath.

Stir in:

Pour the base into an ice cream maker and freeze as directed. When the ice cream is almost frozen, stir in the remaining 1 cup toasted coconut. Transfer to a container with a tight-fitting lid and freeze for at least 4 hours to harden.