Preheat oven to 350 degrees FCream together butter and sugars until smooth and fluffy. This can take up to 3-4 minutes. Add eggs, lemon zest and lemon juice and mix with a wooden spoon until well combined.
In a separate bowl, sift flour, baking soda, and salt together.
Add flour mixture to the butter mixture and mix until combined.
Using a cookie scoop, drop dough onto a parchment-lined baking sheet so the cookies are 1-2 inches apart. Chill for at least an hour or even overnight. If chilling overnight, cover with plastic wrap so the cookies don't dry out.
Bake cookies in the preheated oven for 10-12 minutes or until cooked through and the bottom of the cookies are lightly browned.Cool cookies completely (you don't want them warm at all).
Whisk together powdered sugar, lemon juice and lemon extract. Add water 1 teaspoon at a time until you reach your desired consistency. You want the icing to be quite thick so don't thin it much if you an help it.
Dip the tops of the cookies into the icing or spoon the icing over the top. Add lemon zest over the tops before the icing dries onto the cookies.
