Preheat the oven to 375 degrees F (190 degrees C). Line a baking sheet with parchment paper.
In a large bowl with a hand or stand mixer with a paddle attachment cream the Unsalted Butter (1/2 cup) and Granulated Sugar (1 cup) until light and fluffy. Scrape down the bowl as necessary.
In the same bowl combine the Egg (1), Sour Cream (1/2 cup), Vanilla Extract (2 teaspoon), and 1 tsp of zest and 1 Tbsp juice from the Lemon (1). Mix until fully combined.
In a separate bowl, mix the Gluten-Free All-Purpose Flour (2 1/2 cup), Kosher Salt (1 teaspoon), Baking Powder (1 teaspoon), and Baking Soda (1/2 teaspoon). Add the dry mixture to the wet ingredients on low speed until combined.
Using an ice cream scoop (1/4 cup), place the batter on a baking sheet 1 inch apart. Use an off-set spatula to flatten the batter until about 4 1/2 inches in diameter circles and ½-inch thick. Bake for 9-12 minutes until the edges start to brown.
Cool on the baking sheet for 5 minutes, then remove from the baking sheet and allow to cool fully on a wire rack.
To make the vanilla icing, combine the Powdered Confectioners Sugar (1 1/2 cup), Light Corn Syrup (1 tablespoon), Lemon Juice (1 teaspoon), Vanilla Extract (1 teaspoon), and Water (2 1/2 tablespoon) until smooth.
Divide the icing evenly between two bowls.
Combine the Dutch Processed Cocoa Powder (1/4 cup) with half of the icing and stir to combine. It should be thick but spreadable. If it's too thick, add hot water. If it's too thin, add more powdered sugar.
Turn the cooled cookies flat side-up and frost the vanilla first, then the chocolate after. Let the frosting set before serving.