Preheat the oven to 350ºF. Line a 9x13-inch pan with parchment paper and spray with nonstick cooking spray.
In a medium bowl, whisk together the flour, baking soda, and salt; set aside.
In the bowl of a stand mixer fitted with the paddle attachment, cream the butter and both sugars together until light and fluffy, about 2 minutes. Add the egg, followed by the vanilla.
Add half of the flour mixture and half of the sour cream. Mix on low until just combined. Add the remaining flour mixture and sour cream, and continue mixing on low until combined. Spread batter evenly into the lined baking pan. Bake in the oven for 12-15 minutes.
Make the icing: In a large mixing bowl, whisk the butter and vanilla together. Add 1 cup of the powdered sugar along with 4 Tablespoons of milk/cream. Whisk in the remaining powdered sugar and 1-2 Tablespoons milk/cream. You want it to be smooth, yet spreadable--not runny.
Remove about 1/3 cup of the icing to a separate bowl. To the 1/3 cup of icing, whisk in the cocoa powder and 1-2 Tablespoons of milk/cream. Transfer to a pastry bag fitted with a medium round tip, or a ziplock bag with the tip cut off.
To Assemble: Spread the white icing evenly over the cookie sheet. Pipe the chocolate icing in a line from one end to the other. Keep piping lines about an inch apart until you reach the bottom. Using a skewer, drag across all of the lines, alternating directions from up to down.