Preheat the oven to 350 F. Line two baking sheets with parchment paper. Set aside.

In a medium bowl, whisk together the flour, baking soda, and salt. Set aside.

In a large bowl, beat the butter until creamy, about 2 minutes. Add the sugar and beat until light and fluffy, about 3 minutes.

Add in the egg and vanilla and beat until combined. Add the flour mixture in three batches, alternating with the buttermilk, beginning and ending with flour.

Using a cookie scoop, scoop the dough onto the prepared baking sheets, spacing them 2 inches apart. Bake the cookies until the bottoms are golden, about 10 minutes. Let the cookies cool completely on the baking sheets.

In a medium bowl, whisk the powdered sugar, corn syrup, lemon juice, vanilla, and water until it's smooth and has a consistency slightly thicker than honey. If needed, add a little more water.

Transfer half of the icing to a separate bowl and mix in the cocoa powder.

Assembly

Flip the cookies over so that the flat side is facing up.

Use an offset spatula to spread a layer of white icing on half of each cookie. Then, spread a layer of chocolate icing on the other half. Let the icing set for 30 minutes before serving.