
Preheat the oven to 350°F. Line a 9x13-inch baking pan with parchment paper.
In a medium bowl, whisk together the flour, cornstarch, ginger, cinnamon, baking soda, salt, allspice, cloves, and nutmeg.
In a large mixing bowl, whisk to combine the brown sugar, melted butter, granulated sugar, and molasses until smooth. Add the eggs and vanilla and whisk together until the mixture is thick and well combined.
Add the dry mixture to the wet mixture and stir with a spatula until combined.
Transfer the dough to the prepared baking pan and spread into an even layer.
Bake for about 30 to 32 minutes or the top is set, the edges start to pull away from the sides of the pan and a toothpick inserted into the center comes out clean. Let the bars cool completely in the pan.
In a large mixing bowl with a handheld electric mixer or the bowl of a stand mixer with the paddle attachment, beat the butter and cream cheese on medium speed for about 1 minute until creamy. Add the powdered sugar, vanilla, and salt. Beat on low speed just until combined. Then, increase to medium speed for about 2 minutes until light and creamy.
Spread over top of the cooled gingerbread bars. Garnish with slices of candied ginger or sprinkles if you like.