Preheat the oven to 350 degrees F and line 2 cookie sheets with parchment paper.
In a bowl of a stand mixer fitted with a paddle attachment, cream together the butter, sugar, and lemon zest on medium high speed for about 2 minutes. Scrape the sides, if needed.
Add the egg and vanilla and cream again for 2 more minutes.
In a medium mixing bowl whisk together the flour, baking powder and baking soda.
Add the flour mixture to the stand mixture and mix until almost combined.
Add the sour cream and buttermilk and mix until just combined. It should be about as thick as a very thick pancake batter.
Scoop about 5-6 cookies per cookie sheet in ¼- 1/3 cup size scoops. Try to make the batter scoops on the sheet as round as you can. Using an ice cream scoop or large cookie scoop helps this a lot. The cookies will be as round as the batter when they go in the oven.
Bake for about 15-17 minutes until the edges are starting to brown.
Remove from the oven and let cool on cookie sheet for 5 minutes before removing to a wire cooling rack.
To make the glaze, add the powdered sugar to a medium mixing bowl. Whisk in 3 tablespoons of boiling water, corn syrup, and vanilla. Continue whisking until you have a thick but spreadable frosting. If you need to, add another tablespoon of water. Don’t make the frosting too thin.
Flip each cooled cookie over and frost half of each cookie with the frosting, making a nice line on the halfway mark of the cookie.
Place on a wire cooling rack to set up a bit.
Then, add the melted chocolate and cocoa powder to the remaining frosting and whisk until combined. If it is too thick or freezes up, add a few tablespoons of hot water until it is a spreadable consistency.
Frost the other half of the cookies with the chocolate glaze and let set a few minutes before serving.