In a large bowl, cream together butter and white and brown sugars by hand or with a mixer. Gradually add eggs, one at a time, then add molasses and 2 tablespoons of the candied ginger. Mix well and set aside.
In a medium bowl, sift together the flour and all spices. Gradually add the flour mixture to the butter mixture and form a slightly stiff but still soft dough.
Turn out the dough onto a lightly floured surface and form into two small rectangular loaves. Place on a large baking sheet lined with parchment paper or a silicon baking mat and bake for 20 minutes.
After loaves are finished baking, remove from the oven and reduce oven to 300F/148C degrees. Let the loaves cool on the baking sheet for 5 minutes. Remove the loaves from the baking sheet and cut into ½-3/4" slices on the diagonal with a sharp knife and place slices laying flat back on baking sheet. Bake for additional 15-20 minutes.
Transfer biscotti to a wire rack and let cool completely. Once biscotti has completely cooled, dip one side of each slice into melted chocolate and sprinkle with the reserved chopped candied ginger. Place back on wire rack to dry.
Store leftover biscotti in an airtight container 4-6 weeks (if they last that long!)