How to Make It
To prepare pudding, combine 3 cups milk, rice, 1/3 cup sugar, and butter in a medium saucepan; bring to a boil. Reduce heat; simmer, uncovered, for 10 minutes, stirring occasionally. Remove from heat.
Combine 1/2 cup milk and egg, stirring with a whisk. Gradually stir about one-fourth of warm rice mixture into egg mixture; add to pan, stirring constantly. Simmer, uncovered, for 30 minutes or until rice is tender, stirring occasionally. Remove from heat; stir in vanilla.
To prepare syrup, squeeze juice from the pomegranate halves using a citrus reamer or juicer to measure 1 cup. Combine juice and 1/4 cup sugar in a small saucepan; bring to a boil. Reduce heat; simmer until reduced to 1/3 cup (about 20 minutes), stirring frequently.
Drizzle the syrup evenly over pudding, and sprinkle with seeds.