Beat butter and sugar 2 minutes; add molasses and egg. Separately whisk flour, ginger, cinnamon, cloves, baking soda, and salt.
Mix dry into butter just until combined. Form two discs; wrap and refrigerate 2 hours, additional to listed active time.
Heat oven to 350°F; parchment-line sheets. Roll dough between parchment to 1/4 inch thick; cut about 36 small 2 1/2-inch shapes, rerolling scraps once.
Space 1 inch apart; bake in three batches 9 to 10 minutes each until edges firm and centers no longer damp.
Cool on sheets 5 minutes; rack-cool completely before packing.