Place rice in a bowl; cover with water to 1 inch above rice. Stir until water becomes cloudy; drain. Repeat procedure until water no longer becomes cloudy.
Place rinsed rice and 2 cups water in a 2-quart saucepan; bring to a boil over medium-high heat. Cover, reduce heat, and simmer 15 minutes or until liquid is absorbed. Remove from heat; let stand 10 minutes. Uncover and stir well.
Place cardamom, clove, and cinnamon on a double layer of cheesecloth. Gather edges of cheesecloth together; tie securely. Add cheesecloth bag, 1 cup water, milk, sugar, and salt to rice; stir well to combine. Bring to a boil over medium-high heat, stirring frequently. Reduce heat, and simmer until reduced to 4 cups (about 20 minutes). Remove cheesecloth bag; discard.
Place egg yolk in a small bowl. Add 1 tablespoon rice mixture; stir well to combine. Combine egg mixture and rice mixture; cook over medium-low heat 3 minutes, stirring constantly. Remove from heat; stir in vanilla. Sprinkle with ground cinnamon, if desired. Serve warm.