Set a fine-mesh sieve in a large bowl set over a blow of ice water.

In a large saucepan, whisk the coconut milk and agave syrup over moderately low heat until warm. In a medium heatproof bowl, whisk the sugar and cocoa powder. Gradually whisk in 1 cup of the warm coconut milk until smooth, then whisk in the egg yolks. Scrape the cocoa paste into the saucepan and whisk until blended. Cook the custard over moderate heat, whisking constantly for 6 minutes until very hot and slightly thickened; do not let it boil. Immediately strain the custard into the prepared bowl and stir in the vanilla. Stir the custard until chilled.

Freeze the custard in an ice cream maker according to the manufacturer's directions. Transfer the ice cream to a large plastic container and freeze until firm, at least 4 hours.

In a small skillet, toast the coconut flakes over low heat until lightly browned, 4 minutes. Transfer to a plate and let cool. Serve the ice cream topped with toasted coconut.