Add the butter to a large bowl, and mix it until smooth.
Add in the sugar, and vanilla extract, and beat for about 2 minutes, until light and creamy.
Add in the flour, cornstarch, and salt. And stir it all together until the flour is mixed in. Try not to overwork the batter, and stir until just combined.
Place the dough onto plastic wrap and roll it into a ball, covered in the plastic wrap.
Place the dough into the fridge to chill for 1 hour.
Preheat the oven to 350 degrees Fahrenheit. Line a cookie sheet with parchment paper.
Transfer the dough to a lightly floured surface, and use a rolling pin to roll the dough to be between 1/4 and 5/16inch thick.
Cut the dough into 2-3 inch cookies (using cookie cutters, or a knife). Get the cookies dough cuts as close together as you can so you don't have to rework and reroll the cookie dough too much.
Carefully transfer the cut out cookies onto the prepared baking sheet, and place them about 1 inch apart from each other.
Bake the cookies in the oven for 10-12 minutes, or until the bottom of the edges are just beginning to turn a light golden brown color. Watch closely for the last couple minutes as the color can turn dark quickly.
Let the cookies cool for 5 minutes on the baking sheet, then transfer them to a cooling rack to cool completely.