Preheat oven to 350 degrees F. Line a baking sheet with parchment paper or grease it with non-stick cooking spray.
In a large mixing bowl, beat the shortening, brown sugar, and egg together until light and fluffy, about 1-2 minutes.
In a medium mixing bowl, stir together flour, baking soda, salt, cinnamon, cloves, and nutmeg.
Stir half of the dry ingredients into the wet ingredients. Next, stir in apples and raisins. Then stir in the remaining half of the dry ingredients and milk until well combined.
Drop heaping tablespoons of batter onto the prepared baking sheet 2 inches apart. (The cookies will spread.)
Bake for 10-12 minutes, until the edges are golden brown and set. Remove from the oven and let rest on the pan for 3-5 minutes before transferring them to a wire rack to cool completely.
Once the cookies are cooled, make the glaze by whisking together the powdered sugar, butter, vanilla, and half and half in a medium mixing bowl until smooth.
Spread or drizzle the glaze over the cookies. Then let them rest so the galze can set up. Store in an airtight container.