Preheat the oven to 350°F. Line a baking sheet with parchment paper.
To make the dough: In the bowl of a stand mixer fitted with the paddle attachment, add the butter, cane sugar, dark brown sugar, molasses, and vanilla extract. Mix on low until combined and there are no chunks of butter. Add the eggs and mix just slightly, enough to break the yolks.
In a separate bowl, add the dry ingredients: flour, cinnamon, cloves, ginger, baking soda, and sea salt and whisk together. Add the dry mixture to the butter mixture and mix on low until a stiff dough forms.
Transfer the dough to the prepared baking sheet. Using your hands form a large log out of the cookie dough and flatten slightly so it’s about 1-inch thick, it should be about 13 x 3 inches. Sprinkle the 2 tablespoons of cane sugar over the top of the cookie log.
Bake for 35 minutes or until the middle looks set, but not completely done. Remove from oven and let rest for 15 minutes.
Trim off the edges, then slice into 12 pieces and separate them to reveal the cut sides so they can get some air flow and crisp up during the second bake.
Bake again for 20 minutes. Allow to cool completely on the baking sheet.
Store in a cool dry place for up to 7 days.