Beat butter and brown sugar for 2 minutes, then beat in molasses and egg. Whisk flour, ginger, cinnamon, cloves, baking soda and salt in a second bowl.
Mix the dry ingredients into the butter mixture just until combined. Divide into two discs, wrap and refrigerate for 2 hours, additional to the listed active time.
Heat the oven to 350°F and line baking sheets with parchment. Roll the dough between parchment to 1/4 inch thick and cut into approximately 36 small 2 1/2-inch shapes, rerolling scraps once.
Arrange 1 inch apart and bake in three batches for 9 to 10 minutes each, until the edges are firm and the centers no longer look damp.
Cool on the sheets for 5 minutes, then transfer to racks and cool completely before packing.