In a large bowl, cream softened butter and sugar for 2-3 minutes, until fluffy and combined. Add in eggs, vanilla, lemon extract, and lemon zest. Keep mixing to combine.
Stir in flour, baking soda, baking powder, and salt. Mix until combined.
Drop dough balls onto a lined baking sheet with parchment paper or a silicone mat. Bake for 10-11 minutes or until down in the center. Let cool before icing.
Zested Glaze
Combine all of the glaze ingredients in a bowl. The consistency will be a little on the thick side so it can set on the cookies. Add more milk if it is too thick to stir.
When the cookies are cooled, use a spoon to pour a little glaze on top of the cookie, using the back of the spoon to spread. You can also just dip your cookie facedown, letting excess icing drip off. Sprinkle extra lemon zest on top and let set for at least an hour! ENJOY!