Preheat the oven to 400°F.

In a large bowl, whisk together the flour and brown sugar. Cut the butter into pieces, and using two forks or your fingers, work the butter into the flour mixture until it's the consistency of wet sand. Press the cookie dough firmly and evenly into a non-stick quarter size (9x13 inches) rimmed baking sheet.

Bake the shortbread for 10 to 15 minutes until it is pale golden. Remove the shortbread from the oven, place it on a cooling rack and allow it to cool completely while still in the pan. Once it has cooled, use a sharp knife to carefully cut around the edges then invert the shortbread cookie onto your serving platter.

In the bowl of a stand mixer fitted with the paddle attachment, blend the cream cheese until it is smooth. Add the butter and continue blending until combined. Add the vanilla extract then sift the powdered sugar into the bowl and blend just until combined. (Over-blending the mixture will cause the frosting to be too runny.)

Spread the cream cheese frosting in an even layer on the cookie cake. Position the blueberries in the top left corner of the cake in even rows to form the blue portion of the flag then position the raspberries in horizontal lines across the cake, leaving about 1 inch between each row, to form the stripes. Position the white chocolate chips between the blueberries to form the stars.

Using a sharp knife, slice and serve the cookie cake immediately, or refrigerate it until ready to serve.