Preheat the oven to 350 degrees F. Line two cookie sheets with parchment paper. Set aside.
Cream butter and sugar in a large bowl.
Now add the vanilla, egg, lemon zest, and lemon juice to the bowl, continue to beat until combined.
Mix the flour, baking powder, soda, and salt in a small bowl, whisk with a fork until combined. Now add this dry mixture to the wet mixture slowly, continuing to mix until combined.
You can use a cookie scoop or tablespoon to drop the cookie dough into balls into a bowl of confectioners' sugar one at a time, then transfer them to the cookie sheets.
Place in the oven and bake for about 9-11 minutes. The cookies should be crackly on top when done.
Remove from the oven and allow to cool on pan for a few minutes. Then transfer the cookies to a cooling rack. Continue to cool.
Mix the confectioners' sugar and milk together in a small bowl. You can add more of either ingredient until you get the desired consistency you like for a glaze. Now drizzle the glaze over the cookies. Allow the glaze to dry.
Serve with a big old lemon loving smile!