Preheat oven to 325F and line a 9x13 metal baking pan with parchment paper leaving the sides high to pull out easier once baked.
In a medium bowl whisk together all-purpose flour, ground ginger, cinnamon, baking powder, allspice, cloves, and sea salt. Set aside.
In a large mixing bowl, add sugars, melted butter, and molasses. Mix well using a spatula until most of the butter is absorbed. (You can use a stand mixer if preferred).
Add Greek yogurt, egg, additional egg yolk, and pure vanilla extract, then mix again until well combined (about 30 seconds on low if using a stand mixer).
Transfer dry ingredients to the mixing bowl, and mix until there are no dry streaks, then transfer the dough to the prepared baking pan.
With an offset spatula (or metal spoon) flatten the cookie dough as evenly as you can, then bake for about 22 minutes, or until a toothpick come out of the center with moist crumbs.
Cool on a wire rack fully then start your frosting.
To the bowl of a stand mixer add half of the icing sugar, cream cheese, butter, vanilla extract, ground allspice and cinnamon. With the paddle attachment, start on low and move the speed up to medium and run until most of the icing sugar is mixed in.
Add the remaining icing sugar to your preference and mix until smooth. If you feel you’ve gone too far, add small amounts of milk until you reach your desired consistency. (4 cups/520 grams is my preference, it is a stiffer frosting, so I put it on while the cookies are still in the pan, and I have to lightly press the sprinkles in to stick).
Slice and serve as desired.