Preheat the oven to 325°F (163°C). Line two baking sheets with parchment paper.
In a large bowl, cream the softened butter and granulated sugar together until light and fluffy, about 3-4 minutes.
In a separate bowl, whisk together the all-purpose flour and salt.
Gradually add the flour mixture to the butter mixture, mixing until just combined and a dough forms.
Turn the dough out onto a lightly floured surface and roll it to about 1/4 inch thickness.
Use a cookie cutter or knife to cut the dough into desired shapes and place them on the prepared baking sheets about 1 inch apart.
Bake the cookies for 20-25 minutes or until the edges are lightly golden.
Remove the cookies from the oven and allow them to cool on the baking sheets for 5 minutes before transferring to a wire rack to cool completely.
While the cookies cool, prepare the icing by whisking together the powdered sugar, milk, and vanilla extract in a small bowl until smooth.
Once the cookies are completely cooled, spread or drizzle the icing over the top of each cookie.
Allow the icing to set for at least 30 minutes before serving or storing.