Cinnamon Sugar Walnuts:
1 egg white
1 cup large walnut pieces
2 tablespoons sugar
1/2 teaspoon ground cinnamon
For the Walnut Apple Spice Cake:
1 tablespoon plus 3/4 cup (1 1/2 sticks) unsalted butter, room temperature
2 medium Granny Smith apples, peeled, cored, cut into 1/2-inch pieces
2 medium Jonagold apples, peeled, cored, cut into 1/2-inch pieces
1 3/4 cups all purpose flour
1 teaspoon ground cinnamon
1 teaspoon baking soda
1/2 teaspoon ground allspice
1/2 teaspoon ground cloves
1/2 teaspoon salt
1 1/4 cups sugar
1 large egg
1 cup toasted walnuts, chopped
1 cup dried currants (optional)
For the Icing:
1 8-ounce package cream cheese, room temperature
1/2 cup (1 stick) unsalted butter, room temperature
1 cup (packed) powdered sugar
1 teaspoon vanilla extract
1 generous teaspoon dried currants (if desired)
For the Walnuts:
Preheat oven to 375°F. Line large baking sheet with foil. Beat egg white (reserve yolk for another use) in medium bowl until foamy. Mix in remaining ingredients.
Spread walnuts in single layer on prepared sheet. Bake until walnuts are golden, about 10 minutes. Cool on baking sheet. Transfer walnuts to work surface and chop coarsely.
For the Cake:
Melt 1 tablespoon butter in heavy large saucepan over medium-low heat. Add all apples; cover and simmer until apples are juicy and almost tender, stirring occasionally, about 18 minutes. Uncover and simmer until almost all juices evaporate, about 6 minutes. Using potato masher, mash apples in pan. Cool.
Position rack in center of oven and preheat oven to 350°F. Butter and flour two 8-inch-diameter cake pans with 1 1/2-inch-high sides. Whisk flour and next 5 ingredients in medium bowl. Using electric mixer, beat remaining 3/4 cup butter and sugar in large bowl until light and fluffy. Beat in egg. Beat in half of flour mixture on low speed, then all of applesauce, then remaining flour mixture. Mix in 1 cup toasted walnuts and currants.
Divide batter between pans; smooth tops. Bake cakes until tester inserted into center comes out clean, about 40 minutes. Cool cakes in pans on racks 5 minutes. Turn cakes out onto racks and cool.
For the Icing:
Using electric mixer, beat cream cheese and butter in large bowl until fluffy. Add powdered sugar and vanilla and beat to blend.
Place 1 cake layer on plate; spread 1/2 cup icing over top. Top with second cake layer. Spread remaining icing over top and sides of cake. Arrange cinnamon-sugar walnuts in ring 1/2 inch in from edge of cake, or any way you would like. Sprinkle walnuts with currants (if using). Chill cake until icing sets, about 30 minutes. (Can be prepared 1 day ahead. Cover with cake dome and keep chilled. Bring to room temperature before serving.) Serve, accept the praise you will receive for your beautiful effort, and ENJOY!