Preheat oven to 350 degrees. Line a few large baking sheets with parchment paper. Set aside.
To a stand mixer fitted with a paddle attachment, add butter, granulated sugar and brown sugar and mix on medium speed for 4 minutes until light and fluffy. Turn mixer to low and add eggs, one at a time, making sure each egg is fully blended before adding the next, and scraping down the bowl as needed. Add the molasses and fresh ginger and continue to mix for 1 minute until thoroughly combined. Remove bowl from mixer.
In a medium bowl, whisk together flours, ground ginger, baking soda, cinnamon, cloves and salt. Add this dry mixture to the wet ingredients, stirring until just combined with a few streaks of flour. Add in burnt sugar shards, stirring until evenly distributed.