In the bowl of an electric mixer fitted with the paddle attachment, mix together shortening, brown sugar, applesauce, and molasses until well combined.
In a medium bowl, whisk together flour, baking soda, cinnamon, ginger, cloves, and salt. Slowly add flour mixture to shortening mixture; mix until combined. Transfer dough to refrigerator and let chill for 1 hour.
Preheat oven to 375 degrees. Line a baking sheet with parchment paper; set aside.
Using your hands, form dough into 1-inch balls. Place granulated sugar in a shallow dish; roll each ball in sugar. Place on prepared baking sheet and sprinkle a few drops of water onto each ball using your fingers.
Transfer baking sheet to oven and bake until lightly browned, 12 to 14 minutes. Let cookies cool completely on baking sheet before serving.