Preheat your oven to 350°F (175°C). Line baking sheets with parchment paper.
In a large bowl, cream together the softened butter and granulated sugar until light and fluffy.
1 cup unsalted butter
Beat in the eggs one at a time, then stir in the vanilla extract.
1 cup unsalted butter
In a separate bowl, whisk together the flour, baking soda, and salt.
1 cup unsalted butter
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Stir in the lemon zest.
1 cup unsalted butter
Drop rounded tablespoons of dough onto the prepared baking sheets, about 2 inches apart.
Bake for 8-10 minutes, or until the edges are lightly golden. Let the cookies cool on the baking sheets for a few minutes before transferring them to a wire rack to cool completely.
To make the frosting, whisk together the powdered sugar, lemon juice, and milk until smooth. Add lemon extract if using.
1 cup unsalted butter
Once the cookies have cooled completely, spread or drizzle the frosting over them.
Notes
Store cookies in an airtight container at room temperature for up to 3 days.