Heat oven to 350° F.
Beat the butter and sugar in the bowl of an electric mixer on medium-high until smooth. Add the molasses and egg and beat until fluffy, about 2 minutes. Reduce speed to low.
Combine the flour, baking soda, ginger, cinnamon, cloves, and salt, then add slowly to the butter mixture, mixing until just incorporated. Shape into a flat disk. Refrigerate, wrapped, for 30 minutes.
Roll out the dough on a floured surface to 1/4 inch thick. Cut into shapes and place on lined baking sheets. Bake 10 to 12 minutes, until firm. Cool slightly on the sheets before transferring to cooling racks.