In a medium bowl, whisk together the flour, baking soda, salt, ginger, cinnamon, allspice, cloves, and black pepper.
In the bowl of an electric mixer fitted with the paddle attachment or beaters, beat the butter and sugars on medium speed until light and fluffy, about 2 minutes. Beat in the egg and molasses.
Add the flour mixture and mix on low speed until combined. Divide the dough in half and shape into two discs. Wrap the discs in plastic wrap and chill in the refrigerator until firm, at least 1 hour or up to three days.
Meanwhile, preheat the oven to 350°F ; set two racks near the middle of the oven. Line two baking sheets with parchment paper.
Remove the dough from the refrigerator. (If the dough has been in the fridge for longer than an hour, you'll need to let it sit out at room temperature for 10 to 15 minutes and knead it briefly until it is supple enough to roll.) Place the dough on a lightly floured work surface. Dust more flour over the dough. Roll, turning and adding more flour under and over the dough as necessary, to about 1/8-inch thick (or for softer cookies, roll to 1/4-inch thick). Cut out shapes with a cookie cutter and transfer the cookies to the prepared baking sheets, using a spatula if necessary. Gather the dough scraps and knead into a ball, then roll out and cut again, adding more flour as necessary. Repeat until scraps are used up.
Bake the cookies, rotating the sheets from top to bottom and front to back midway through, for 8 to 10 minutes or until they feel firm. Let the cookies cool on the baking sheets for several minutes until set, then transfer to a rack to cool completely. Repeat with the remaining dough.
When the cookies are completely cool, decorate with icing. Let the icing set completely, a few hours, then store in an airtight container.
Freezer-Friendly Instructions:The Cookie Dough can be Frozen for up to 3 Months: Shape the dough into 2 discs, wrap each securely in plastic wrap, and place them in a sealable bag. When ready to bake, remove the disks from the freezer, thaw the dough until pliable, and then proceed with recipe. To Freeze After Baking: Let the cookies cool completely and store in an airtight container separating layers with parchment paper or aluminum foil. Before serving, remove the cookies from the container and let them come to room temperature.