Preheat oven to 350°F. Butter an 8-inch square metal baking pan and lightly dust with flour, shaking out any excess.
In a bowl, whisk together flour, baking soda, cinnamon, allspice, salt and cloves; set aside.
Cream butter and sugars in bowl of an electric mixer, beating at high speed until fluffy, about 5 minutes. Add egg and beat well until blended. Mix in applesauce at low speed, then add flour mixture, mixing at low speed until incorporated. Stir in walnuts and raisins. Scrape batter into prepared pan and bake 40 minutes, until cake tester inserted in center comes out clean. Let cake cool completely in pan.
Make frosting: Beat cream cheese and butter together until smooth. Add sugar and vanilla extract and mix until blended. Spread frosting on cooled cake and cut into 6 pieces.