Step 1: Preheat your oven to 350°F (175°C) for even baking.
Step 2: Line a baking sheet with parchment paper to prevent sticking.
Step 3: In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.
Step 4: In a large bowl, cream the butter and sugar with an electric mixer until light and fluffy, about 3-4 minutes.
Step 5: Add the egg and vanilla to the butter mixture and beat until fully incorporated.
Step 6: Mix in the sour cream until smooth and creamy.
Step 7: Gradually add the dry ingredients to the wet ingredients, mixing just until combined.
Step 8: Scoop rounded spoonfuls of dough onto the prepared baking sheet, spacing them 2 inches apart.
Step 9: Bake for 12-15 minutes, until edges are golden and centers are set. Cool on the baking sheet before transferring to a wire rack.
Step 10: In a medium bowl, combine powdered sugar, 3 tablespoons of milk, corn syrup, and vanilla for the icing. Mix until smooth.
Step 11: Divide the icing in half and mix cocoa powder into one half for the chocolate icing.
Step 12: Spread vanilla icing on one half of each cookie and chocolate icing on the other half. Allow to set for 30 minutes before serving.