Preheat the oven to 350°F. Line a large baking sheet with parchment paper and set aside.
In a large bowl, beat together the softened butter and white sugar until fluffy. Add the egg, sour cream, and vanilla extract, and beat until well combined.
Add the baking soda and baking powder, and mix. Finally, add the flour and beat until everything is fully incorporated. The dough will be very thick—don’t worry, that’s how it should be!
Scoop the dough using a tablespoon and roll into balls. Place them on your prepared baking sheet, leaving a decent amount of space between each one (I usually bake 5–6 cookies per sheet). Gently flatten each ball of dough with your hand.
Bake for 10–12 minutes, or until the bottoms and edges of the cookies are a light golden brown. Remove from the oven and gently flatten each cookie with the bottom of a glass or jar. (If your cookies already spread and flattened enough for your liking while baking, feel free to skip this step. I usually do it to make sure they’re all the same thickness.)
At this point, I always like to reshape my cookies using a wide-mouth canning jar ring to make them nice and round, but feel free to skip this step.
Allow the cookies to cool slightly on the baking sheet before transferring to a wire rack. Repeat with the remaining dough.
Once the cookies are completely cooled, make the icings.
In a small bowl, combine powdered sugar and whole milk for the white icing. Whisk until smooth. Add the clear vanilla extract, if using, and whisk again. Add more milk as needed to create a smooth, runny icing. Set aside. In a separate bowl, combine powdered sugar and whole milk for the black icing. Whisk until smooth. Add the cocoa powder and whisk to combine. Again, add more milk as needed to create a smooth, runny icing. Using the back of a spoon, carefully spread a layer of white icing over half of each cookie. (Some people dip their cookies, but I find frosting them gives the best results.)
Allow the white icing to harden completely before adding the black icing.
Once the white side is dry, frost the remaining half with black icing—again, using the back of a spoon.
Let the black icing harden completely, then serve and enjoy!