Heat oven to 375° F. Cream the butter and 1 3/4 cups sugar in a large bowl with an electric mixer on high speed. Lower to medium and add the eggs, molasses, vinegar, and vanilla. Sift together the flour, baking soda, salt, ground ginger, cinnamon, cloves, cardamom, and pepper. With the mixer on low, slowly add the flour mixture to the butter mixture. Beat until incorporated. Fold in the crystallized ginger. Divide the dough into 3 equal portions (it will be sticky). Place each portion on a sheet of plastic wrap and form into a 12-inch log, 2 inches in diameter. Wrap and chill for 1 hour. Slice each log into disks, 1/2 inch thick. Dredge in the remaining sugar. Place on a parchment- or foil-lined baking sheet, 2 inches apart. Bake until crinkly around the edges, about 14 minutes. Let cool on sheets for 5 minutes, then transfer to wire racks.