In a 2 quart, heavy saucepan blend together the brown sugar, cornstarch, cocoa powder, and salt. In a small bowl, whisk the coconut milk, whole milk, and egg yolks to combine. Gradually whisk the milk mixture into the sugar and cocoa mixture.
Set the saucepan on the stove, over medium heat, and cook, stirring constantly, until the pudding thickens and bubbles. Lower the heat a little and let it bubble away for about a minute. Remove from the stove and add the chopped chocolate. Whisk gently until the chocolate melts and blends into the mixture. Add the rum.
Pour the pudding into dessert dishes, cover the surface directly with plastic wrap, and cool. Place in the refrigerator to chill. When ready to serve, whip a quantity of heavy cream to soft peaks. Dollop over the puddings and sprinkle with the toasted coconut chips. Refrigerate any leftovers.