Stir together all the ingredients except the nuts, mixing well until the sugar dissolves. Transfer to an ice cream maker and follow the manufacturer's directions. When the mixture is the proper consistency, remove from the ice cream maker and fold in the nuts. Transfer to a covered container and freeze at least 24 hours.

The day of:
Preheat the oven to 375* F.
Grease two muffin tins, skipping every other cup, so that you have six cups of each tin greased (you may also use clean tuna cans with the bottoms and tops removed) and set aside.

In a medium mixing bowl, combine the oil, sugar and eggs. In a large mixing bowl, combine the cinnamon, salt, flour, baking soda and cardamom. Add the wet ingredients to the dry ingredients and combine (mixture should be fairly thick). Gradually stir in the rum, then fold in the apples.

Bake for 25-30 minutes or until a toothpick inserted into the center of a cake comes out clean. Allow to cool for ten minutes in the pans, then turn out onto a cooling rack and cool to room temperature.

Assembly:
Place the cakes in the center of twelve dessert plates and top each with a one-ounce scoop of toasted walnut ice cream. Drizzle the syrup over the ice cream and cake, garnish with mint and serve.