1. Bring 1 1/2 cups water to a boil in a medium saucepan; add rice. Cover, reduce heat, and simmer 20 minutes or until tender.
2. Scrape seeds from vanilla bean; add vanilla bean seeds and pod to rice. Add 1 cup milk, sugar, and salt to rice mixture in pan. Cook over medium heat 15 minutes or until thick and creamy. Remove and discard vanilla bean pod.
3. Combine 1/4 cup milk and egg in a small bowl. Slowly add egg mixture to rice mixture; cook 2 minutes over medium heat, stirring constantly. Remove from heat; stir in butter and cinnamon. Serve warm, or pour into a 2-quart dish; cover surface of pudding with plastic wrap, and chill overnight.