Preheat the oven: Preheat the oven to 350°F and line two baking sheets with parchment paper. This keeps the cookie bottoms from over-browning.
Cream butter and sugar: In a large bowl, beat the softened butter and brown sugar together until light and fluffy, about 2 minutes. Add the molasses and egg, beating until smooth and fully combined.
Whisk the dry ingredients: In a separate bowl, whisk together the flour, baking soda, ginger, cinnamon, cloves, salt, and cornstarch. Breaking up any clumps here helps the spices distribute evenly.
Combine wet and dry: Add the dry ingredients to the wet mixture and stir just until no flour streaks remain. The dough should be soft and slightly sticky.
Scoop the dough: Scoop the dough into balls about 1.5 tablespoons each, rolling them smooth between your palms.
Roll in sugar: Roll each dough ball in granulated sugar until fully coated, then place on the prepared baking sheets about 2 inches apart.
Bake the cookies: Bake for 9 to 11 minutes, until the edges are set but the centers still look soft and slightly puffy. Avoid overbaking, since the cookies firm up as they cool.
Cool on the pan: Let the cookies rest on the baking sheet for 5 minutes before transferring to a wire rack. This short rest lets them finish setting without breaking apart.
Store for softness: Once fully cooled, store the cookies in an airtight container at room temperature to keep them chewy for days.