How to Make It
Make the cake: Preheat the oven to 350°. Lightly butter a 9-by-13-inch baking dish. In a bowl, sift together the flour, baking soda, cinnamon, salt and nutmeg.
Using a standing electric mixer fitted with a paddle or a handheld electric mixer, beat the butter, oil and sugar on high speed until thoroughly combined. Add the eggs one at a time, beating well after each addition. Add the vanilla and beat until light and fluffy, 3 to 4 minutes.
Beat in the dry ingredients on medium speed just until blended. Fold in the apples. Spread the batter in the prepared dish and bake for about 50 minutes, or until golden and a cake tester inserted in the center comes out clean. If the top browns too quickly, cover loosely with foil during the last 20 minutes. Let the cake cool slightly on a rack.
In a saucepan, bring the maple syrup, butter, cream and salt to a boil over moderate heat. Boil rapidly for 1 minute. Let cool slightly. Cut the apple cake into pieces and serve warm with the maple sauce and vanilla ice cream.