In a heavy-bottomed pot, combine milk, rice, sugar, and butter. Cook, stirring constantly, over low heat until thickened, about an hour. During the last 15 minutes of cooking, add cinnamon and cloves.
In a small bowl or measuring cup, beat eggs and vanilla. Slowly temper the eggs, adding a small amount of the heated milk and whisking constantly until the eggs have come up to warm room temperature in order to avoid scrambling. Once eggs are tempered, add egg-milk mixture into the pudding, stirring to combine completely. Pour into a serving bowl or individual serving cups to cool. Top with ground cinnamon and serve warm or refrigerate and enjoy cold.