Whisk the dry ingredients: In a medium bowl, whisk together the flour, ground ginger, cinnamon, cloves, baking soda, and salt until evenly combined. Set the bowl aside.
Melt the butter: Melt the butter in a microwave-safe bowl or small saucepan, then let it cool for a few minutes so it won't cook the egg when mixed in.
Combine the wet ingredients: Whisk the melted butter with the brown sugar, molasses, and egg until smooth and glossy, about 1 minute.
Mix the dough: Add the dry ingredients to the wet mixture and stir with a spatula just until no streaks of flour remain. The dough will be soft and slightly sticky.
Chill the dough: Cover the bowl and refrigerate for 45 minutes to 1 hour, until the dough is firm enough to roll into balls without sticking to your hands.
Preheat the oven: About 15 minutes before baking, preheat the oven to 350°F and line two baking sheets with parchment paper.
Portion the dough: Scoop out tablespoon-sized portions of dough and roll each one into a smooth ball between your palms.
Coat in sugar: Roll each dough ball in granulated sugar until fully coated, then place them on the prepared sheets about 2 inches apart.
Bake until cracked: Bake for 9 to 11 minutes, until the tops crack and the edges look set but the centers still look slightly soft and underdone.
Cool on the pan: Let the cookies rest on the hot baking sheet for 5 minutes; they will continue to firm up slightly without drying out.
Transfer to a rack: Move the cookies to a wire rack to finish cooling completely before storing.