Preheat the oven to 350° F and line two baking sheets with parchment paper.

Whisk together the flour, baking powder, salt and baking soda in a small bowl. Set aside.

Cream the butter, sugar and lemon zest in a stand mixer on medium-high speed until light and fluffy, about 5 minutes.

Add the eggs and vanilla and beat on medium-high speed until combined, about another minute. Scrape down the sides of the bowl with a spatula.

Alternate adding the dry ingredients and sour cream to the bowl, beginning and ending with the dry ingredients, mixing after each addition and scraping down the sides as necessary. Mix just until combined.

Measure out ¼ cup batter and place it on the prepared cookie sheet. Repeat until you have four cookies per sheet. (Aim for 1.75 to 2 ounces of weight per cookie.) Spread each mound of batter in the shape of a circle until the batter is approximately ½ inch thick. Repeat with the second baking sheet.

Bake the cookies for 12 to 14 minutes, rotating the tray 180 degrees halfway through baking. Cool cookies on the sheet briefly then remove the cookies to a wire rack to cool. Repeat with the remaining dough. Allow the cookies to cool completely before attempting to ice them.

To make the icing, whisk together the powdered sugar, 4 tablespoons of milk, the corn syrup and the vanilla in a medium bowl. The icing should be thick but spreadable.

Turn the cookies over so the flat side (or the bottom of the cookie) is facing up. This is the side you will glaze. Spread the white icing on one half of each cookie in a thin, even, opaque layer using a small offset spatula or knife. Place cookies on a wire rack, icing-side up, and allow the icing to harden completely before proceeding with the chocolate icing. (Cover the bowl so the remaining icing does not dry out.)

Add the cocoa powder to the remaining white icing. Add 2 tablespoons milk to the mixture and whisk until the icing has reached a thick but spreadable texture. (If the mixture is not sweet enough to your liking, or you are running low after glazing the cookies with the white icing add a ¼ cup more of powdered sugar and more milk if necessary.)

Glaze the second half of each cookie and allow the icing to harden completely before storing the cookies.

Store cookies in an airtight container for up to 3 days.