Make the Gingerbread Cookie Bars:
Preheat your oven to 350°F (175°C). Grease a 9×13-inch baking pan with non-stick spray or line with parchment paper.
In a medium bowl, whisk together the flour, ground ginger, cinnamon, nutmeg, cloves, and baking soda.
In a separate large bowl, cream together the softened butter and brown sugar until fluffy.
Beat in the molasses and vanilla extract, followed by the egg and egg yolk, until fully combined.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Press the cookie dough into the prepared pan, using lightly greased hands if necessary.
Bake for 22-25 minutes or until the edges start to pull away from the pan and a toothpick inserted comes out clean.
Allow the cookie bars to cool completely in the pan before frosting.
Make the Cream Cheese Frosting:
In a large mixing bowl, beat the softened butter until light and fluffy.
Add the cream cheese and beat until smooth.
With the mixer on low speed, gradually add the powdered sugar, one cup at a time, alternating with 1 tablespoon of whipping cream or milk. Continue beating until the frosting reaches your desired consistency and sweetness.
Spread the frosting evenly over the cooled gingerbread cookie bars. Optionally, top with festive sprinkles.