Place the chocolate in a microwave-safe bowl and microwave in 30-second intervals, stirring in between, until melted and smooth. Cover and set aside.
Heat the coconut milk and 1 ¼ cups water in a medium pot over medium-high heat until it begins to steam, about 2 minutes. Meanwhile, pulse the sugar, eggs, salt, potato starch, and cocoa in a food processor until combined. Add 1 cup of the hot coconut milk in a steady stream and pulse again. Return the warm egg mixture to the pot with the remaining coconut milk and cook over medium-high heat, whisking constantly, until thick and glossy and beginning to bubble. Remove the pan from the heat and whisk in the melted chocolate and the vanilla extract.
Divide the pudding among six cups and cover tightly with plastic wrap. Refrigerate until very cold, at least 4 hours. Top with coconut before serving.