Combine first 4 ingredients in a medium bowl; stir until sugar dissolves. Pour into an 11 x 7-inch baking dish. Cover and freeze 45 minutes. Stir with a fork every 45 minutes until completely frozen and slushy (about 3 hours).
Combine milk, sugar, and vanilla in a small bowl, stirring until sugar dissolves. Cover and freeze 45 minutes. Stir milk mixture with a fork every 30 to 45 minutes until completely frozen and slushy (about 2 hours).
To serve, remove orange mixture and milk mixture from freezer; stir each mixture with a fork until fluffy. Spoon orange ice into 6 small dishes; top with cream ice.