Preheat oven to 350 degrees F. Grease a 9 X 13-inch pan.
For the cake- beat together oil, milk, and eggs in a medium bowl. Mix in dry ingredients. Gently stir in vanilla.
Pour half of the batter into the prepared pan. Lay ½ of the apple slices over the batter to create a colorful pattern.
For the Crumb Topping- place brown sugar, granulated sugar, cinnamon and butter in a medium bowl. Cut butter in with a pastry blender or work with your hands until crumbs the size of peas form. Mix in the nuts.
Cover apples with a thin layer of crumb topping. Layer the remaining apples. Spread remaining batter over apples and top with remaining crumb topping.
Bake for 60-70 minutes, or until golden brown and a toothpick inserted in the middle comes out clean.
For the Syrup topping- combine the syrup and the cream in a heavy saucepan and heat, stirring frequently.
Serve cake warm or at room temperature with warm syrup topping.