Preheat oven to 350℉. In a medium bowl, mix together flour, baking soda and salt.
Use a hand mixer to beat the butter and sugar together in a large mixing bowl for about 3 minutes or until it's evenly distributed. Then, add in the eggs and vanilla.
Gradually beat in flour mixture one cup at a time, and add in buttermilk mixture between each cup of flour, and mix until smooth. Be sure to scrape down the sides of the bowl.
Spoon roughly ¼ cup of batter onto a baking sheet lined with parchment paper. Make sure the cookies are several inches apart.
Bake on the middle rack for 15 minutes, or until they are springy and the bottom is golden brown.
Stir together icing sugar, corn syrup, lemon juice, vanilla, and 1Tbsp of water in bowl until smooth. Pour half of this mixture into another bowl and add in the cocoa powder. (You might have to add a little more water to make it spreadable).
Turn cooled cookies flat side up, and spread icing with pastry spatula, or butter knife. White over one half, chocolate over the other.