In a medium, heavy-bottomed pot, over medium heat, bring milk, cocoa powder, rice, brown sugar and salt to a boil; stirring occasionally; the cocoa powder will not incorporate fully until the milk is warm.
Immediately reduce the heat to medium-low to maintain a gentle simmer.
Cook, stirring often, until the milk has reduced, thickened and the rice is very tender; about 20 minutes.
Remove the pot from the heat and stir in the egg yolks, maple syrup and vanilla; it will look loose at this point but will thicken as it cools.
Serve warm or chilled, with whipped cream and a sprinkle of cocoa, if you like.
Safe to refrigerate, in an airtight container, for up to 2 days.
