Whisk together 2 cups all-purpose flour, ½ teaspoon baking powder, ½ teaspoon baking soda, and ½ teaspoon salt in a medium mixing bowl.
In the bowl of your mixer, cream ¾ cup unsalted butter and 1 cup granulated sugar until light and fluffy, about 2 to 3 minutes.
Mix in 2 large eggs, zest from 1 lemon, and 1 teaspoon vanilla extract. Slowly add the flour mixture just until combined.
Mix in ½ cup buttermilk.
Scoop the cookie dough with a 3-tablespoon cookie scoop and arrange on a sheet pan, about 3 inches apart. Refrigerate for 30 minutes to allow the dough to firm up. Lightly press down on the cookie dough to flatten.
Heat oven to 350°F and line 2 sheet pans with parchment paper.
Bake the cookies for 13 to 16 minutes until the edges are firm. Allow the cookies to cool completely.
In a medium mixing bowl, combine 2 cups powdered sugar, 1 tablespoon light corn syrup, 1 tablespoons hot water, and ¼ teaspoon vanilla extract. Add more water if the frosting is too thick; it should be thick enough to hold its shape without spilling off the sides of the cookies, but still be spreadable.
Pour half of the frosting into a separate bowl and stir in ¼ cup Dutch process cocoa powder.
Flip the cookies over and frost half of the bottoms with the vanilla frosting. Let the frosting sit for at least 5 minutes, to begin to set and form a crust, then frost the other half with the chocolate frosting.
Allow the frosting to set completely and enjoy.