In a medium mixing bowl, whisk together the flour, cornstarch, soda, salt, cinnamon, cloves and ginger. Set aside.
In a large mixing bowl combine the butter and brown sugar. Beat on medium until the mixture is light and fluffy. Add the molasses and vanilla and blend until smooth. Add the egg and beat until blended. Scrape down the sides and bottom of the mixing bowl and blend again to incorporate.
Add about 1/3 of the flour mixture and mix on low until incorporated. Repeat until all flour is blended. Add the candied ginger and blend on low just until incorporated. Scrape the sides and bottom again with a rubber spatula, and blend one more time. Cover the mixing bowl and refrigerate 1 hour.
Preheat oven to 350 degrees. Line two baking sheets with parchment paper. Pour about 1/4 cup of the coarse or granulated sugar into a shallow bowl for rolling.
Scoop out some of the cookie dough using a 1-inch cookie scoop or tablespoon. Roll the dough into a ball, then roll the ball in the coarse sugar.
Place the cookies on the baking sheet at least 2 inches apart and freeze for 15 minutes. Bake the cookies in a preheated oven for 10-12 minutes. Remove the cookies from the oven, and using the back of a 1/2 teaspoon measuring spoon, make an indentation in the center of each warm cookie. Transfer to a cooling rack and let cool completely. Fill with 1/2 teaspoon of the caramel filling. Cool until set, about 30 minutes.