Creamy Rice and Apple Pudding

2 1/2 C milk
3/4 C quick-cooking rice
1/4 C packed light brown sugar
1/2 tsp salt
2 eggs, lightly beaten
1/2 C coarsely chopped (peeled) apple (about 1 small apple)
1 1/2 tsp vanilla extract
1/4 C coarsely chopped walnuts

In a medium saucepan, combine milk, rice, sugar, and salt; bring to a boil. Reduce heat and simmer, uncovered, for five minutes, stirring occasionally. Beat two tablespoons hot rice mixture into the eggs, beating constantly; stir this mixture into rice mixture remaining in saucepan. Stir in chopped apple. Cook and stir over low heat for 30 seconds longer; do not boil. Remove from heat, stir in vanilla extract, and pour into a large serving bowl or individual serving dishes. Cover and refrigerate until thoroughly chilled. Sprinkle with chopped nuts before serving.