Whisk 2 cups plus 2 tablespoons flour, ground ginger, cinnamon, baking soda, salt, cloves, black pepper, and cayenne together in a large mixing bowl until thoroughly mixed.
Cream together butter and 2/3 cup sugar in a separate bowl until pale yellow and creamy, about 2 minutes. Add candied ginger, molasses, vanilla, and egg. Whisk mixture until well blended. Add dry ingredients to butter/sugar mixture and stir just until the flour disappears. Cover dough with plastic wrap and refrigerate until chilled, about 1 hour.
Preheat oven to 350 degrees F (175 degrees C). Line a baking sheet with parchment paper. Pour 1/2 cup white sugar in a shallow dish for rolling cookies.
Scoop out about 1 1/2 teaspoons dough with a small scoop or teaspoon. Form dough into balls and roll in white sugar. Place cookies on prepared baking sheet. Slightly flatten cookies to about 1/4 inch thick; sprinkle with a pinch more sugar.
Bake in preheated oven until cookies are your desired crispiness or chewiness, 10 to 15 minutes.
