Heat oven to 175 degrees F. Generously butter a 1 1/2-quart-tall souffle dish and a wide strip of parchment paper to form a collar extending at least 3 inches above the rim of the dish. Press the collar, buttered side inward, against the inside of the dish. Chill until butter is set and the paper sticks to the dish. To extract the zest from the skins of the oranges, rub them with the sugar cubes so that the cubes soften and turn bright orange. Wrap the sugar cubes in plastic wrap, and crush them with a rolling pin. Set an apple 1/2, cut side down, on a board and cut it crosswise into the thinnest possible slices, about 1/8-inch thick. Alternately, slice apple halves using a mandoline. Sprinkle bottom of souffle dish with sugar. Arrange a layer of apple slices in a floral pattern in the bottom of the souffle dish. Top this first layer of apple with more apples slices arranged across the others like ripples in a pond. (This crossed pattern of slices ensures that the cake holds together when unmolded.) Sprinkle the second layer with the crushed orange sugar. Continue filling the souffle dish until the apples, held in place by the paper collar, extend at least 3 inches above the rim. (They will shrink down into the souffle dish during baking.) Cover them with a round of parchment paper. Top with a small stack of plates slightly smaller than the souffle dish to seal and weigh down apples. Bake until apples are much reduced and meltingly soft when pierced with a skewer, 12 to 14 hours. Tear off the top of the paper collar, and let the cake cool to room temperature. Combine mascarpone and yogurt in a small bowl. Unmold cake onto a warm platter. The top should be lightly caramelized with a little syrupy juice running down the sides. Serve warm, with caramel sauce and mascarpone-yogurt combination.
In a medium heavy-bottomed saucepan, heat sugar, lemon juice, and 1/2 cup water over low heat until the sugar dissolves. Bring the syrup to a boil, and continue to boil without stirring until it begins to turn golden around the edges. It is important not to stir, as the syrup may crystallize. Meanwhile, combine butter and heavy cream in a small saucepan. Heat until the butter melts. When the syrup begins to color, lower the heat a bit, and continue boiling to a deep-golden color. It will darken rapidly. Remove the pan from the heat, and let it cool for 30 seconds. Add the butter and cream, being careful as the syrup will bubble up in the pan. Place pan back over heat, stirring until the caramel is completely dissolved. Let the sauce cool, taste, and add a pinch of salt, if necessary. Serve hot or chilled. Yield: 6 servings