Bring water, cinnamon sticks, anise seed and lemon zest to a boil. Continue boiling until reduced in volume by half. Strain into a stainless-steel pot.
Add rice and salt and cook, uncovered, over moderate heat until all of the liquid has be absorbed, about 45 minutes.
Stir in heavy cream and milk. Continue cooking about 2 hours or until thickened.
Stir in sugar and vanilla extract. Chill in individual serving dishes or a large casserole dish.
Makes: 4