Make the cake In a large bowl, toss the apples with the Calvados, ginger, cinnamon and 2 tablespoons of the sugar. Let stand for 30 minutes.

Preheat the oven to 350°. Brush a 9-inch springform pan with butter. 

In a large bowl, using a hand mixer, beat the 3 sticks of butter with the remaining 2 1/4 cups of sugar and the salt until pale yellow and fluffy, about 3 minutes. Beat in the eggs one at a time until smooth. Using a wooden spoon, stir in the flour and baking powder until a thick, smooth batter forms. Fold in 8 of the apple slices. Spread the batter in the prepared pan. 

Arrange the remaining apples in slightly overlapping concentric circles on the batter and drizzle on the apple juices. Bake for about 1 hour and 40 minutes, until a cake tester inserted in the center comes out clean.  

Meanwhile, make the glaze In a small saucepan, combine the sugar with 2 tablespoons of water and bring to a simmer without stirring. Cook over moderate heat, swirling the pan, until an amber caramel forms, about 4 minutes. Carefully add the cream and butter (the mixture will sputter) and cook, whisking, until the caramel is smooth, about 2 minutes. 

Transfer the cake to a rack and let stand for 10 minutes. Unmold the cake and brush the top with the glaze. Let cool slightly and serve warm or at room temperature.