Bring 3 cups water and 1/4teaspoon salt to boil in heavy largesaucepan.
Add rice and boil 10 minutes.
Drain rice; discard cooking water. Rinsesaucepan.
Combine milk and sugar in samesaucepan; bring to boil over medium-highheat, stirring until sugar dissolves.
Addrice; reduce heat to medium and simmeruntil rice is very tender, most of milk isabsorbed, and pudding is thickened but stillcreamy and reduced to scant 3 cups, stirringoccasionally, about 35 minutes.
Removefrom heat. Stir in vanilla extract.
Transferrice pudding to medium bowl. Press plasticwrap onto surface of pudding; let puddingcool to room temperature. Refrigerate untilcold. DO AHEAD: Can be made 2 days ahead.Keep refrigerated.
Peel apples; quarterthrough stem end and remove core.
Cuteach apple quarter into 4 slices, then cutslices crosswise into thirds.
Combine sugarand lemon juice in medium nonstick skillet.Stir over medium-high heat until sugardissolves and syrup is medium amber color,occasionally swirling skillet, 3 to 4 minutes.
Remove from heat; add butter to skilletand swirl until melted (mixture may bubblevigorously). Return skillet to medium heat;add cider and pinch of salt and bring toboil.
Add apples and simmer until tender,stirring often, about 6 minutes.
Add 1/2cup whipping cream and boil until saucethickens slightly, about 2 minutes.
Transferapples with caramel sauce to heatproofbowl. Cool caramel apples until lukewarmor room temperature. DO AHEAD: Caramelapples can be made 1 day ahead. Cover andrefrigerate. Stir over medium heat until justwarm before using.
Divide half of caramel apples among6 Martini glasses or lowball glasses. Topeach with rice pudding, dividing equally.Top with remaining caramel apples,dividing equally.
Garnish each with dollopof whipped cream, if desired, and serve.