Resist eating this cake fresh out of the oven. The flavor reaches its peak when refrigerated overnight.
Heat the oven to 325 degrees. Brush a 10-inch springform pan with soft butter. Coat the pan with 1/4 cup superfine sugar, lightly tap out excess sugar, and set pan aside.
Combine 1 cup butter and remaining 2 cups superfine sugar in bowl of an electric mixer fitted with a paddle attachment. Beat on medium speed, scraping down the sides with a rubber spatula, until mixture is light and fluffy, about 5 minutes. Carefully fold in the applesauce. Do not overmix.
Sift together 2 3/4 cups flour, 1 teaspoon cinnamon, 1/4 teaspoon nutmeg, cloves, salt, and baking powder. Fold the dry ingredients and pecans into the applesauce mixture. Add the vanilla, Calvados, and apple slices, and mix until just combined.
Transfer the batter to the prepared springform pan. Combine the remaining 3 tablespoons butter, 3 tablespoons flour, 1/2 teaspoon cinnamon, 1/4 teaspoon nutmeg, brown sugar, and ginger in a small mixing bowl. Mix with fingers until just combined, and sprinkle lightly over the batter. Place cake in oven, and bake until a cake tester inserted into the center of the cake comes out clean, about 1 hour and 50 minutes. Let stand until completely cool.