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

Beat the butter on medium speed using a hand or stand mixer until it is light and fluffy.

Turn the mixer to low speed and add the powdered sugar and lemon zest.

Mix until well incorporated, scraping down the sides of the bowl as needed.

With the mixer on low speed, gradually add the flour. 

Next, add the milk and lemon extract. 

Keep mixing until a shaggy dough forms, about 1 minute.

Form the dough into a disk and wrap it in plastic wrap.

Refrigerate for 15 minutes. This will help make the dough easier to roll and cut. 

On a lightly floured surface, roll out the chilled dough until it is 1/4 inch thick.

Using a cookie cutter of your choice, cut out the cookies and place them on the baking sheets. I used a round cookie cutter and got 10 cookies.

Place the sheets in the freezer for 10 minutes to chill the dough. This prevents spreading. 

Bake until the edges of the cookies are golden brown, about 12-14 minutes.

Transfer to a wire rack to cool and then store in a plastic container at room temperature for up to 3 days.