Preheat oven to 350 degrees F. Line two baking sheets with parchment paper; set aside.
In the bowl of a stand mixer, cream together the butter and granulated sugar with the paddle attachment for 2 minutes or until fluffy and pale in color. Add in the egg and vanilla and mix well, scraping down the bottom and sides of the mixing bowl periodically to ensure everything is well blended. Meanwhile, sift together the flour, baking powder, baking soda, and salt in a medium bowl. Add in 1/3 of the flour mixture, mixing well and scraping the bowl if needed. Add in half of the sour cream, mix well. Repeat, alternating flour and sour cream and ending with flour until the batter is soft. It won't be as thick as traditional cookie dough - almost like a cross between cake batter and cookie dough.
Using a 1/4 cup size cookie dough scoop, portion the cookie dough 3" apart on the baking sheets. You should get exactly 12 scoops of cookie dough, 6 per sheet. Bake for 15-18 minutes, rotating pans halfway through baking time to ensure even cooking for both trays. Cool on the baking sheets.
For the icing: In a large bowl, combine the sifted confectioners' sugar, 6 Tablespoons of the whole milk, the corn syrup, vanilla extract, and salt and whisk until thickened and combined. Remove one cup of the icing to a separate small bowl and to the small bowl add the remaining Tablespoon of milk and the sifted cocoa powder, stirring until combined.
Using an offset spatula, spread half of the flat side of the cookie with vanilla icing. Let vanilla icing set for about 15-20 minutes. Then frost the other half of the cookie with the chocolate icing. Allow cookies to set, about 1 hour, before serving.