Combine milk with salt, butter, lemon zest, vanilla and sugar. Bring to a boil over low heat, stirring occasionally. Add rice and allow to boil briefly. Cook covered, stirring frequently, on low heat for 40-45 minutes until rice thickens.
Peel and quarter apples, core and grate finely. Add to rice pudding during last 5 minutes of cooking.
Sprinkle with cinnamon sugar and serve.