Rinse cranberries thoroughly. In a medium sauce pot, bring apple juice and cranberries to a low boil; cover with a lid. Continue to cook until you see most of the cranberries "pop" (broken open). Remove from heat.
Pour cranberries in a food processor (or high powered blender) with the sugar and half of the coconut milk. Run until smooth; transfer mixture back to sauce pot and bring to a low simmer.
Mix the cornstarch with the remaining coconut milk and slowly stir into the cranberries. Add the vanilla (if using), and continue to cook, stirring continuously. When the sauce starts to thicken and swell (like a pudding), remove from heat.
Pour into a medium bowl and cover with plastic wrap, making sure that it touches the cranberries (to prevent a layer of film). Refrigerate at least 4 hours or overnight.
To serve: divide into serving cups or small bowls, top with dairy-free whipped cream. You can also alternate layers of cranberry sauce with whipped cream, if desired (pictured).