Heat oven to 350°F. Line 2 half-sheet pans with parchment paper and set aside.
Whisk together the flour, baking soda, ground ginger, cardamom, cloves, and salt in a medium mixing bowl.
Cream the brown sugar and butter in a stand mixer fitted with the paddle attachment and beat on low speed until light and fluffy, 1 to 2 minutes. Add the molasses, egg, and fresh ginger, and beat on medium speed for 1 minute. Add the candied ginger and, using a rubber spatula, stir to combine. Add the dry ingredients to the wet and stir until well combined.
Using a 2-teaspoon-sized scoop, drop the dough onto the prepared half-sheet pans, approximately 2 inches apart. Bake on the middle rack of the oven for 12 minutes for slightly chewy cookies or 15 minutes for crisper cookies, rotating the pan halfway through baking.
Remove from the oven and leave the cookies on the sheet pan for 30 seconds before transferring to a cooling rack to cool completely. Repeat with all of the dough. You will use each pan approximately twice.
Store in an airtight container for up to 10 days. If desired, you may scoop and freeze the cookie dough on a sheet pan and, once frozen, transfer to a zip-top bag to store. Bake directly from the freezer, following the above procedure.