Peel, core and coarsely chop the apples. In a large saucepan, combine the apples, 1/2 the sugar, a pinch of cinnamon and 4 tablespoons of the apple juice. Cover, and simmer slowly until the apples are soft, but don't let them break down, then transfer to a casserole dish.
Melt the butter in a saucepan over moderate heat. Add the rice, let cook for 2 to 3 minutes stirring frequently. Add the remaining apple juice, bring to a boil, then reduce to a simmer, simmering until the apple juice has been absorbed and rice is tender; about 20 minutes. Stir occasionally.
Stir in a teaspoon or so of sugar to rice, and let rice cool for about 10 minutes. Stir the cream into the rice, spoon rice mixture over apples. Sprinkle the remaining sugar over the top, and place under a hot broiler (aka grill in the UK) until sugar has carmelized and is a dark, golden brown.
You can serve this warm, or chilled.
For heavy cream, you can use whipping cream, double cream, clotted cream or mascarpone.