In a large bowl, whisk together the butter, sugar, applesauce, and molasses until well combined, then set aside.
In a small bowl, whisk together the flour, ginger, cinnamon, cloves, baking soda, and salt. Add the dry ingredients to the wet ingredients and stir using a rubber spatula until just combined.
Using a medium (1½-tablespoon) spring-loaded cookie scoop, scoop the dough into balls and place the dough balls on a parchment paper-lined baking sheet. Loosely cover with plastic wrap, and place in the refrigerator to chill for 15-20 minutes.
Preheat the oven to 350°F (180°C) while the cookie dough is chilling.
Roll each dough ball in sugar, if using, and bake for 10-12 minutes or until lightly browned on the sides. Remove from the oven and allow to cool on the baking sheet for 5 minutes, then transfer to a cooling rack to cool completely.