In bowl, whisk flour, ginger, baking soda, cinnamon, salt and cloves.
In large bowl, using electric mixer on medium speed, beat butter with 1 cup sugar until creamy and light, about 3 minutes. Beat in egg and grated ginger (if using), scraping bottom and side. Beat in molasses.
Beat in half of the flour mixture on low speed, then beat in the remaining half. Scrape into large piece of plastic wrap, folding over and flattening slightly. Refrigerate until firm, about 2 hours or up to overnight.
Preheat oven to 350°F. Line 2 baking sheets with parchment paper. Using a 2 tbsp scoop, portion out dough and roll into balls. Roll each ball in bowl of the remaining ½ cup sugar to coat.
Place on baking sheets 2 in (5 cm) apart and bake until puffed and rounded, 9 to 10 minutes. Let cool on pan for 10 minutes. Transfer to racks and let cool completely.
Sprinkle with flaked sea salt and/or pieces of crystalized ginger. Let cookies set at room temperature for 5 minutes; refrigerate until completely set.