Preheat oven to 325F. Butter and flour a 10" Bundt pan.

Using an electric mixer, blend together the oil and sugar in a large bowl. Add eggs, one at a time, beating well with each addition. Sift flour, soda, salt, nutmeg, and cinnamon into the egg mixture, beating thoroughly. The batter will be very stiff. Fold the apples and walnuts into the batter with a spatula. Stir in the vanilla.

Spoon the batter into the prepared pan. Bake for 1 1/4 hours or until a toothpick comes out clean. Place on a rack and let cool for about 1 hour.

To make the caramel sauce: Melt the butter in a heavy-bottomed saucepan set over medium heat. Stir in the brown sugar. When the sugar dissolves, add the cream, whisking to form an emulsion.

To unmold the cake, run a knife around the edges of the pan and gently turn out the cake onto a plate. Pour about 1/2 of the caramel sauce over the cake to form a glaze. Serve immediately with a little of the sauce spooned over each slice.

may be reheated.