Whisk flour, crystallized ginger, baking soda, and 1/4 teaspoon salt in medium bowl, set aside.
Using electric mixer, beat butter in large bowl until creamy and light, about 2 minutes. Gradually beat in brown sugar. Beat on medium-high speed until creamy, about 3 minutes. Add egg, molasses, fresh ginger, ground ginger, cinnamon, and cloves, one at a time, mixing thoroughly between each addition. Add flour mixture in 2 additions, beating on low speed just to blend between additions.
Place sugar in small bowl. Measure 1 tablespoon dough. Roll into ball between palms of hands, then roll in sugar in bowl to coat; place on baking sheet, lined with parchment. Repeat with remaining cookie dough, spacing cookies 1 1/2 to 2 inches apart.
Bake cookies in center rack until surfaces crack and cookies are firm around edges but still slightly soft in center, about 15 minutes. Cool completely on sheets on rack.