In a bowl, either measure or weigh the flour, baking powder, and salt together (I run a whisk through them to blend), then set the bowl aside. In another bowl, weigh or measure the white sugar and set it aside.
Zest 2 large or 3 small lemons into a bowl. Don't go very deep; you want the yellow, not the underlying white, which can be bitter. Then cut the lemon in half and juice your lemons into another small bowl. With 2 large lemons, I got about ⅓ cup of lemon juice.
Cream the sugar and butter on a medium mixer speed for about 3 minutes. Next, add the vanilla extract, lemon zest, and lemon juice blending for about 1 minute. Then scrape down the bowl and add the egg.
Add half of the flour mixture and blend until incorporated. I stop the mixer and scrape down the sides. Add the milk and blend for about 30 seconds before adding the rest of the flour mixture. Don't over-mix. You can always finish with a spatula if needed. The cookie dough is soft, so stick the bowl into the refrigerator for about 30 minutes.
Line 2 cookie sheet pans with parchment paper, and using a small cookie scoop, put 12 small mounds onto the cookie sheet. Bake at 350°F (175°C or 180°C) for 10-12 minutes. My cookies were done in 11 minutes. Move them to a cooling rack once out of the oven.