In a medium bowl, whisk together the flour and baking soda. Whisk in the ginger, cinnamon, pepper and salt.
Using an electric mixer, cream the butter, granulated sugar and brown sugar on high speed until smooth, light and fluffy, 2 minutes. Beat in the egg for 30 seconds, then mix in the molasses. Scrape down the bowl. Add the flour mixture in 2 batches, mixing on low speed until just combined. Turn out the dough onto a large piece of plastic wrap. Using the wrap to help, form the dough into a disk and seal tightly. Refrigerate the dough for at least 1 hour or up to 1 day.
Preheat the oven to 350 degrees . Line 3 cookie sheets with parchment. Working with 1 tbsp. of dough at a time, mold the dough around each peanut butter cup to enclose completely. Place 12 dough balls on each of the prepared pans. Bake until the tops are just set and slightly cracked, 12 to 14 minutes. Using a spatula, transfer the cookies to a rack to cool for 5 minutes.
Roll the cookies in the confectioners sugar, then return to the rack to cool completely. Roll the cookies in the confectioners sugar again before serving.