Preheat the oven to 375 degrees. Line a baking sheet with parchment paper.
In a large bowl, whisk flour, baking powder and salt together and set aside.
Beat the butter at medium speed and while the mixer is running, gradually add in the sugar. Increase the speed to medium-high and beat until the mixture is light and fluffy, about 3 minutes. Scrape down the sides of the bowl and add the eggs, vanilla and lemon extract. Beat until combined, about 30 seconds. Scrape down the sides and bottom of the bowl again.
With mixer on low speed, alternately add the flour and the milk in three additions (beginning and ending with flour). Mix until just combined.
Use a cookie scoop to scoop mounds of dough onto the prepared baking sheets about two inches apart. Bake until the edges of the cookies are set and light golden brown, about 18 minutes. Allow the cookies to cool for 2 minutes on the baking sheet, then remove to a wire rack to cool completely.
FOR THE ICING:
Whisk the powdered sugar, 6 Tablespoons milk, the corn syrup, vanilla extract, and salt together in a medium bowl. Transfer one cup to another bowl, add remaining tablespoon of milk and the cocoa powder. Whisk to combine.
Once cookies are cooled, flip them over. The flat side will be the side that is frosted. Spread vanilla icing onto half the cookies. Refrigerate for a few minutes or until set. Spread chocolate icing onto other side and allow the icing to set completely before serving.
Cookies will stay fresh in the refrigerator in an airtight container for one week, or they may be frozen for up to three months. Thaw in the refrigerator overnight and then bring to room temperature before serving.