Sift together the flour, ginger, cinnamon, salt, allspice, baking soda, baking powder, black pepper and cloves two times; set aside. In a stand mixer fitted with the paddle attachment, cream the butter and brown sugar on medium speed until light and fluffy, 2 to 3 minutes. Add the molasses, egg and vanilla extract and mix for 3 to 4 minutes. The mixture will look broken but not to worry-it will come together once the flour is added.
Scrape the bowl, add the flour mixture and the candied ginger and mix until combined. The dough will be a bit heavier than a typical cookie dough. Divide the dough into two equal pieces, shape each into a square, wrap in plastic and chill for 1 hour or overnight.
Roll out one square of dough at a time directly on a lightly floured sheet of parchment into a 12-by-12-inch square that's 1/4-inch thick. Repeat with the second piece of dough. Chill both squares until firm, about 30 minutes or overnight.
Line two sheet pans with parchment; set aside. Transfer the well-chilled dough squares to a flat work surface, dusting off any remaining flour with a dry brush. Sprinkle the crushed pieces of caramel candies over the entire surface of one square. With your fingers, even out the surface and then place the second square of dough directly on top, sandwiching the candies.
Roll out the dough into a 14-by-14-inch square that's 1/4-inch thick. Cut out your cookies, placing them on the lined sheet pans. Gather the trimmings, reroll, and cut out as many cookies as possible. (Bake these trimmings for snacking; the dough is too good to waste.) Chill the cookies on the sheet pans one last time until firm, about 30 minutes. Meanwhile, heat the oven to 350 degrees F.
Sprinkle the cookies with the turbinado sugar, then bake for 12 to 14 minutes for crunchy cookies; if you prefer soft cookies, bake for 10 to 12 minutes. Remove from the oven and let cool completely.
Store in an airtight, odor-free container for 3 to 4 days.