Preheat oven to 350 degrees. Grease three 9" cake pans and dust with flour. In a large mixing bowl, combine all dry ingredients. Add melted butter, applesauce and jam to dry ingredients. Hand mix until incorporated; add eggs one at a time and beat by hand until incorporated. Pour cake batter into pans and bake for about 40 minutes until toothpick inserted in middle of cake comes out clean. Move to wire rack and cool completely. Frost cake with either a Caramel or Coconut Pecan Frosting (see below).
Caramel Icing: In heavy sauce pan cook 1/4 cup butter and 3/4 cup brown sugar over medium heat until sugar dissolves and mixture boils. Stir in 1/4 cup heavy cream and bring back up to a boil. Boil for 1 minute. Remove from heat, cool and beat in 2 cups powdered sugar until smooth. Frost cake between, on sides and top of cake.
Coconut Pecan Frosting (my favorite): In a heavy saucepan cook 1 can (14 ounce) Eagle Brand sweetened condensed milk, 3 egg yolks (tempered) and 1/2 cup butter for 10 minutes over medium heat stirring constantly until bubbly. Remove from heat and stir in 1 1/3 cup sweetened flaked coconut, 1 cup chopped pecans and 1 teaspoon vanilla. Allow to cool 15 minutes - frost cake between, on sides and top of cake.