This came from the milk calendar. Make sure you use short grain rice for this recipe to get a creamy pudding. The long grain rice won't cook properly and the pudding won't thicken. The apples and cinnanmon are a nice change from plain rice pudding.
In a deep pan, melt the butter over medium-high heat. Add the apples, half of the sugar, the cinnamon and salt. Cook, stirring, until apples are softened (about 5 minutes). Remove the apples to a bowl.
Put the pan back on medium-high heat. Stir in the rice and sugar.
Whisk the flour into the milk and slowly stir into the rice. Heat until steaming, stirring often.
Reduce heat to low. Cover and simmer for about 25 minutes (until rice is very tender). Make sure you stir occasionally.
Stir in the apples and vanilla. Cool slightly and serve, or chill, and serve cold (the pudding thickens more as it cools). Sprinkle with added cinnamon, if desired.