Preheat oven to 350 degrees. Line a cookie sheet with parchment paper.
In a large bowl, add the butter and sugar. Mix on medium until light and fluffy.
Add in the egg, vanilla, lemon zest, and all but 1 tablespoon of the lemon juice. This will be used in the glaze. Mix on medium until everything is combined.
Add in all of the flour and mix on low until the flour is almost completely incorporated. Turn the mixer to medium and let it go for a minute or two.
Using a cookie scoop, scoop out six cookies to a cookie sheet. Flatten out the cookies. Bake for 10-12 minutes until the bottoms are golden brown.
Remove from the oven and place on a cooling wrap for 15-20 minutes and them dip the tops in the prepared glaze. Place back on the cooling wrack to dry.
Glaze
In a small bowl, add in the powdered sugar, lemon zest, and the reserved tablespoon of lemon juice. Whisk until the powdered sugar is dissolved.