An apple a day tastes even better in cookie form, especially with frosting on top!
In a large mixing bowl, beat butter with an electric mixer on medium to high speed for 30 seconds.
Add granulated sugar, brown sugar, cinnamon, baking soda, nutmeg and cloves. Beat until combined, scraping sides of bowl occasionally. Beat in the egg and apple juice. Beat in as much of the flour as you can, the apple and walnuts. Drop dough by a rounded teaspoon 2 inches apart onto prepared cookie sheet.
Drop dough by rounded teaspoons 2 inches apart onto lightly greased cookie sheets. Bake in a 375°F oven for 10 to 12 minutes or until edges are light brown. Cool on sheets for 1 minute, then transfer to wire racks to cool completely. Frost with Apple Frosting. If you like, sprinkle with freshly grated nutmeg. Store in an air-tight container in refrigerator.
In a medium mixing bowl, beat 4 cups sifted powdered sugar, 1/4 cup softened butter, 1 teaspoon vanilla, and 3 to 4 tablespoons apple juice to make a frosting of spreading consistency.