Prepare a 10-inch bundt pan by spraying with cooking spray.
Peel, core and dice apples. There should be around 2 cups when diced
In the bowl of a stand mixer, or in a bowl using an electric hand mixer, add eggs, sugar, brown sugar, vegetable oil, and vanilla extract.
Beat at low speed about 1 minute.
In a medium bowl, combine flour, baking soda, salt, cinnamon, nutmeg and allspice.
Add dry ingredient mixture to the egg mixture, and using a spoon, stir until combined.
Stir in apples and walnuts.
Spread batter evenly in prepared pan
Bake in center of oven 60 minutes, or until a toothpick inserted in center of the cake comes out clean.
Cool in the pan for about 30 minutes. Remove from pan to a wire rack and pour caramel glaze over the cake, if using. Allow to cool completely
In a glass bowl, melt butter in the microwave, about 30 seconds
Whisk in brown sugar, cream, and vanilla until smooth
Return to the microwave and heat on high about 2 minutes, or until sugar is dissolved
Whisk again and allow to cool
*To toast walnuts, preheat oven to 350°. Spread chopped walnuts on a baking sheet and bake in center of oven for 5 minutes. Remove from oven and allow to cool before using in the recipe. (This can be done while assembling the batter)*I used a non stick bundt pan, but, to be on the safe side, I still sprayed lightly with vegetable oil spray, because there are so many nooks & crannies. If your pan is not a non stick one, you may want to also flour the pan after spraying.