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1
Adjust the oven racks to the upper-middle and lower-middle positions and heat the oven to 350u00b0F. Line 2 large baking sheets with parchment paper. Whisk the flour, baking powder, and salt together in a medium bowl.
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2
In a large bowl, beat the butter and sugar with an electric mixer on medium speed until light and fluffy, 3 to 6 minutes. Beat in the eggs, vanilla, and lemon extract until combined, about 30 seconds, scraping down the bowl and beaters as needed.
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3
Reduce the mixer speed to low and beat in one-third of the flour mixture, followed by half of the milk. Repeat with half of the remaining flour mixture, and the remaining milk. Beat in the remaining flour mixture until combined.
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4
Scoop 1/4-cup mounds of batter onto the prepared baking sheets, spaced about 2 inches apart. Use the back of a spoon or your finger dipped in water to smooth the tops of the cookies. Bake the cookies until the edges are just beginning to turn light golden brown, about 15 minutes, switching and rotating the baking sheets halfway through baking.
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5
Let the cookies cool on the baking sheets for 10 minutes, then transfer to a wire rack and let cool completely, about 1 hour. Repeat with the remaining dough using cooled, freshly lined baking sheets.
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6
Bring the corn syrup and water to a boil in a medium saucepan over medium-high heat. Remove the pan from the heat and whisk in the confectioners' sugar and vanilla until smooth. Measure half of the icing into a separate bowl and whisk in the melted chocolate and 2 to 4 tablespoons of water as needed until the mixture is smooth and spreadable.
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7
Place 2 large wire racks over parchment paper for easy clean up. Spread about 2 tablespoons of the chocolate icing over half of each cookie with a small spatula, then let sit on the wire racks until the icing has just set, about 15 minutes. Spread the vanilla icing over half of each cookie and let sit until the icings have hardened, about 1 hour before serving.
