Preheat your oven to 350°F (175°C).
Prepare a 9x13 rectangular baking pan by greasing it with butter or baking spray, and lining the bottom with parchment paper.
Add the butter to the bowl of your stand mixer fitted with the paddle attachment (or in a mixing bowl, if you're using a hand mixer). Cream the butter on medium high speed until it is soft and creamy and the colour begins to turn pale (use a hand mixer if you wish).
Add the sugar and beat on medium high speed for 2 minutes, scraping down the sides of the bowl a few times.
Beat in the egg on medium high speed, scraping down the bowl after each addition.
Beat in the molasses and scrape down the bowl to ensure everything is evenly combined.
In a separate bowl, combine the flour, baking soda, grated ginger, cinnamon, cloves, and salt. Whisk these ingredients together until they're combined and dump the mixture into the bowl of the stand mixer with the butter mixture.
Combine the butter mixture and the dry ingredients on low speed just until no streaks of flour remain. You'll have to scrape down the sides of the bowl a few times to make sure everything is incorporated.
Press the cookie mixture into the bottom of the baking pan and smooth out the top as much as possible.
Bake for 15-17 minutes at 350°F (175°C) or until the cookie bars lose their shine on top. They will still be soft, especially in the middle, when you remove the pan from the oven.
Let the cookie bars cool completely to room temperature before frosting them.