Heat oven to 350° F. Butter and flour a 9-inch springform or round cake pan.
In a small bowl, combine the flour, baking soda, and salt. In a large saucepan, over medium heat, melt the butter. Remove from heat and stir in the granulated sugar, applesauce, cinnamon, ginger, nutmeg, vanilla, and eggs. Add the flour mixture and stir just until combined. Stir in the raisins. Pour into the prepared pan. Bake the cake until a tester inserted in the center comes out clean, 35 to 40 minutes.
Transfer pan to a wire rack to cool for 10 minutes. Using a knife, loosen the cake from pan. Invert it onto the rack. Turn it over again onto a serving plate. Sprinkle the cake with the confectioners' sugar, slice into wedges, and serve with the ice cream.
In Advance: Bake the cake and let it cool. Set aside at room temperature for up to 24 hours. Cover with foil and warm in a 250° F oven for 30 minutes.
To Freeze: Cool the cake in the pan. Cover the pan tightly with two layers of aluminum foil. Store for up to 3 months.
To Reheat: Refrigerate the cake overnight. Warm in a 250° oven for 30 minutes.