Make the cookie dough. In a medium bowl, whisk together the flour, baking soda, ginger, allspice, cloves, and salt.
In the bowl of a stand mixer fitted with the paddle attachment, combine the sugar and butter. Beat on medium-high speed until light, fluffy, and doubled in volume, 2 to 3 minutes, using a rubber spatula to scrape down the bottom and sides of the bowl as necessary. Reduce the mixer to low and add the egg white and molasses and beat until just combined. Scrape down the bottom and sides of the bowl. With the mixer on low, gradually add the dry ingredients and beat until just combined. Scrape down the bottom and sides of the bowl once more, and beat on low for an additional 30 seconds.
Chill the cookie dough. Cover the bowl and refrigerate the dough for 1 hour, until the dough is scoopable.
Prep the oven and pans. Position a rack in the center of the oven and preheat the oven to 350°F. Line two half sheet pans with parchment paper. Place the sugar for the topping in a shallow bowl.
Assemble the cookies. Use a 1-Tablespoon cookie dough scoop to portion the cookie dough into balls. Roll each in the sugar topping, covering them completely. Place the coated cookies at least 3 inches apart on the prepared sheet pans. Give each cookie dough ball a quick pat with your palm to slightly flatten them. Bake the cookies. Bake one pan at a time for 12 to 15 minutes, or until the edges have set but the centers are still gooey. The cookies will look puffed when you pull them out of the oven, but will fall and crack into the perfect cookies as they cool. Cool the cookies on the pan on a wire rack for 20 minutes, or until the edges and bottoms of the cookies have set and feel firm to the touch. Repeat with the remaining cookie dough.
Serve and store. Serve warm or at room temperature. The cookies can be stored in an airtight container or zip-top bag at room temperature for up to 3 days.