Preheat the oven: Preheat your oven to 400°F (200°C). Then, line two baking sheets with parchment paper or lightly spray them with non-stick cooking spray.
Cream sugar and shortening: In a large mixing bowl, beat ½ cup of shortening and 1 ⅓ cups of packed light brown sugar with a hand mixer or stand mixer on medium speed until the mixture is light and fluffy for about 2-3 minutes.
Add egg: Add 1 large egg to the sugar mixture and beat at medium speed until well combined, for about 1 minute.
Mix dry ingredients: In a medium mixing bowl, whisk together 2 cups of all-purpose flour, 1 teaspoon of baking soda, ½ teaspoon of salt, 1 teaspoon of ground cinnamon, ½ teaspoon of ground ginger, ¼ teaspoon of ground nutmeg, and ¼ teaspoon of ground cloves until well combined.
Combine ingredients: Gradually add the dry ingredients to the sugar mixture, mixing at low speed until dough forms. Scrape down the sides of the bowl as needed to ensure everything is well incorporated.
Add apples, raisins, and applesauce: Gently fold in 1 cup of golden raisins, 2 small shredded apples (about 1 cup), and ¼ cup of applesauce using a spatula. The dough will be very wet, almost like a thick cake batter.
Scoop and bake the cookies: Using a 1½ tablespoon-sized cookie scoop or two spoons, drop scoops of cookie dough onto the prepared baking sheets, spacing them about 2 inches apart. Bake in the preheated oven for 11-13 minutes or until the cookies are golden brown and baked through in the center.
Let it cool: Remove from the oven and let the cookies cool on the baking sheets for 5 minutes before transferring them to a cooling rack to cool completely.
Prepare the icing: In a medium bowl, beat together 1 ½ cups of powdered sugar, 3 tablespoons of softened butter, ½ teaspoon of vanilla extract, and 1-2 tablespoons of cream or milk (start with 1 tablespoon and add more as needed) until smooth and spreadable but thick.
Frost the cookies: Once the cookies are completely cool, use a knife or offset spatula to frost them with the prepared icing.