Preheat the oven to 325°F (163°C). Line a baking sheet with parchment paper.
In a large bowl, cream together the softened butter and granulated sugar until light and fluffy, about 3-4 minutes.
Gradually add the all-purpose flour and salt to the butter mixture, mixing until the dough comes together and is smooth.
Roll the dough into a 1/2-inch thick rectangle on a lightly floured surface.
Cut the dough into 24 equal rectangular or square shapes and place them on the prepared baking sheet about 1 inch apart.
Use a fork to prick the top of each cookie to create a classic shortbread pattern.
Bake in the preheated oven for 20-25 minutes or until the edges are lightly golden.
Remove the cookies from the oven and allow them to cool completely on a wire rack.
While the cookies cool, prepare the icing by whisking together the powdered sugar, milk, and vanilla extract in a small bowl until smooth and pourable.
Once the cookies are completely cooled, spread or drizzle the icing evenly over the tops of the cookies.
Allow the icing to set at room temperature before serving or storing.