Heat oven to 350°F. Spray 2 8-inch round cake pans with baking spray with flour. Line the bottoms of the cake pans with parchment paper. Spray the parchment paper and set aside.
In large bowl, beat butter and sugars with electric mixer on medium speed until light and fluffy. Beat in eggs, one at a time. Stir in vanilla and applesauce. Stir in flour, baking soda, spices and salt. Stir in apples. Spoon into pan.
Bake 40 to 45 minutes on middle rack of the oven until toothpick inserted in center of cake comes out clean. Cool 10 minutes. Remove from pan to cooling rack. Cool 10 minutes longer.
To prepare the frosting: in a stand mixer with a paddle attachment cream the butter and cream cheese until light and fluffy (about 3 minutes). Add in the powdered sugar 1 cup at a time. Add in the vanilla and caramel sauce and mix until combined. Keep the frosting chilled until ready to use. Use an offset spatula to spread a layer of frosting on top of the first layer. Top with the second layer of cake. Spread frosting around the top and sides. Spread more caramel sauce on top and top with toasted chopped walnuts.
Keep cake covered and refrigerated for up to 3 days.