Preheat the oven to 350 degrees F. If you plan to serve the cake on a platter, prepare a 9x13 baking pan by lining with parchment paper. If you plan to serve the cake in the 9x13 baking pan, lightly grease the bottom and sides with butter or baking spray.
In the bowl of a stand mixer, use a paddle attachment to beat the butter, sugar, and brown sugar until combined and becomes a bit lighter in color.
Add the eggs and vanilla, beat until the mixture starts to become light and airy. While the mixer is running, stream the molasses in and continue to beat for a couple minutes.
Add the vinegar and milk, beat until combined.
Turn the mixer off and sift the flour, cornstarch, baking soda, cinnamon, clove, ginger, and salt into the batter. Turn the mixer back on using a medium low speed and mix until combined.
Pour the batter into your prepared 9x13 pan. Bake in the preheated oven for 35-45 minutes. When finished baking, remove from the oven and let cool completely.
When the cake has cooled, prepare the cream cheese frosting. Begin by cutting the softened cream cheese into chunks and place into the bowl of a mixer. Beat on a high speed until it becomes smooth and a little airy.
Reduce speed to medium high. While the mixer is running add a couple tablespoons of the softened butter, once the butter has incorporated into the cream cheese, add a couple more tablespoons of the butter. Continue doing this until all the butter is gone. Whip until light and airy.
Add the salt, vanilla, and half of the powdered sugar, mix on medium speed until fully incorporated. Then add the remaining powdered sugar and whip on high speed until light and fluffy.
If you plan to serve the cake on a platter, remove the cake from the pan and use a long bread knife to slice all of the edges off the cake, this will give it a nice clean look. Frost the top of the cake with a thick layer of the cream cheese frosting.
Sprinkle with festive sprinkles when ready to serve.