Heat oven to 325 degrees F. Brush a 10-inch springform pan with soft butter. Coat the entire 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; mix until just combined.
Transfer the batter to the prepared spring-form 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 crumbly, 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.
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