Preheat oven to 350°F and line two baking sheets with parchment paper.
In a bowl, whisk together flour, baking soda, and salt. Set aside.
In a small bowl, combine buttermilk, vanilla, and lemon extract.
Cream butter and sugar in a large bowl until fluffy. Beat in eggs one at a time.
Alternately mix in dry ingredients and buttermilk mixture into the creamed mixture, starting and ending with dry ingredients.
Drop ¼ cupfuls of dough onto prepared baking sheets, spacing 2 inches apart.
Bake for 15–18 minutes or until edges are golden. Let cool completely.
For icing: In a medium bowl, whisk powdered sugar, corn syrup, vanilla, and water until smooth and thick but spreadable.
Transfer half the icing to another bowl and stir in cocoa powder and a little water to reach desired consistency.
Flip cookies over and spread vanilla icing on one half and chocolate on the other. Let set.