Whisk together the flour, cocoa powder, ginger, cloves, cinnamon, baking soda, salt, and pepper in a mixing bowl. Set aside.
Using a stand mixer fitted with the paddle attachment, beat the butter on medium-high speed until creamy. Slowly add the granulated sugar and mix on medium speed until the mixture is completely smooth and soft. Stop the mixer and scrape down the sides of the bowl with a rubber spatula as needed.
Add the egg and mix well. Add the molasses and corn syrup and beat until incorporated. Stop the mixer again and scrape down the sides of the bowl.
Add the flour mixture and beat on low speed until a dough forms that pulls away from the sides of the bowl and all the ingredients are well incorporated.
Remove the dough from the bowl, flatten it on a large piece of plastic wrap into a rectangle about 1 inch thick, cover the dough with the plastic wrap, and refrigerate overnight.
Preheat the oven to 350 degrees. Line a baking sheet with parchment paper.
Unwrap the dough and place on a floured work surface. If using an embossed rolling pin with a design, roll out the dough 1/3 inch thick, lightly dust the top with flour, roll over the dough, and then cut out the shapes with a small knife and place on the prepared baking sheet, spacing them about 1 inch apart. If using stamps, flour them and stamp the dough, then cut out.
Bake the cookies until lightly golden along the sides but still soft to the touch in the centers, 7 to 15 minutes. The timing will depending on the size of the individual cookies, or if you have made a single large patterned piece that will be cut after baking. Bake them the least amount possible to retain their softness.
Mix one cup of powdered sugar with 2 tbsp of water for the glaze. Thin more if needed.
When the cookies are ready, remove from the oven and let cool on the pan on a wire rack for about 10 minutes. Then dip them in glaze and let drip dry on a cooling rack.