In the large bowl of a standing or handheld mixer, cream the butter and sugar until fluffy, about 2 minutes. Add the egg and continue to beat. Add the molasses and beat well. In a medium-size bowl, whisk together the flour with the baking soda, ginger, cinnamon, salt, and pepper. Add the dry mixture to the wet ingredients; then add the orange zest, and stir just enough to form a smooth dough. Turn the dough out onto a counter lightly dusted with flour, and divide into two equal portions. Gather each portion into a disc shape, wrap in plastic, and refrigerate at least 30 minutes, or up to overnight.
Preheat your oven to 350° and set the racks to the middle positions, with space in between. Line two baking (cookie) sheets with parchment paper. On a counter dusted with flour, roll each disc of dough out to a ⅛-inch thickness, and cut out shapes with your favorite cookie cutters, gathering and rerolling the dough as needed.
Bake until barely golden, about 6 to 8 minutes, depending on size; then cool on wire racks.