Preheat the oven to 350˚F.
Beat the butter with a mixer at medium speed until fluffy; gradually add the sugar, beating well. Add the eggs, 1 at a time, beating just until blended after each addition. Add the apple, beating just until blended.
Whisk together the flour, baking soda, cinnamon, cloves, and salt; add to the butter mixture, and mix just until blended. Stir in the walnuts, if desired.
Pour into a lightly greased 13- x 9-inch baking pan. Bake 30 to 35 minutes or just until a wooden pick inserted in the center comes clean. Let cool on a wire rack 10 minutes. Serve with Homemade Caramel Sauce and, if desired, whipped cream or ice cream.
Caramel Sauce: Cook the sugar, half-and-half, butter, and salt in a small saucepan over medium-low for 5 to 7 minutes, whisking slowly until thickened. Remove from the heat, and let cool slightly before serving.