Combine the rice, sugar, vanilla, cinnamon, 3 cups water, and a pinch of salt in a small pot over high heat. Bring to a boil and reduce heat to a simmer.
Add the coconut milk, return to a simmer, and cook, stirring occasionally, until the rice is tender, 25 to 35 minutes.
Meanwhile, combine the clementines and brown sugar. Serve over the pudding.
Tip: Arborio rice is ideal because it stays pleasantly chewy, but any other white rice would work equally well in this recipe.