Place sugar and milk in crockpot and stir to dissolve sugar. Stir in rice, cinnamon sticks and vanilla. Cover and cook on high for 2 to 3 hours, until the rice is tender. After it starts to simmer, stir it once or twice to make sure rice isn't clumping.

Pour into a serving dish, sprinkle with nutmeg and allow to cool and thicken. Serve chilled.