Preheat the oven to 350 degrees F (176 degrees C) and prepare a cookie sheet with parchment paper (or lightly oil it). Whisk the flour, crystallized ginger, baking soda, and ¼ teaspoon of salt in a medium bowl.
Using an electric mixer, beat the vegan butter and brown sugar in a large bowl until creamy and light. Add applesauce, molasses, fresh ginger, ground ginger, cinnamon, and cloves. Add the flour mixture in two additions, beating on low speed just to blend between additions. If the dough is feeling too dry, add 1 to 2 more tablespoons of applesauce.
Place ¼ cup of sugar in a small bowl. Measure about two tablespoons of dough. Roll into a ball between palms of hands, then roll in sugar in a bowl to coat; place on a baking sheet. Repeat with remaining cookie dough, spacing cookies 1 ½ inches apart.
Bake for about 12 to 15 minutes (check them at the 12 minutes mark). Let cool and enjoy!