Cream the butter and sugar together in a large bowl until the mixture is light and fluffy.
Beat in the egg until fully incorporated.
Combine the flour and salt in a separate bowl.
Gradually add this dry mixture to the wet ingredients, mixing until a dough forms.
Mix in the vanilla extract until it's evenly distributed throughout the dough.
Divide the dough into thirds or quarters and shape into discs.
Wrap each disc in plastic wrap and refrigerate until the dough is firm enough to roll.
This usually takes about 1-2 hours.
Preheat your oven to 350 degrees Fahrenheit.
Lightly grease your cookie sheets or line them with parchment paper.
Roll out one disc of dough at a time to a 1/4 inch thickness on a floured surface.
Cut out shapes using 2- or 3-inch cookie cutters.
Place the cut-out cookies about an inch apart on the prepared cookie sheets.
Bake for 8-10 minutes, or until the edges are just starting to turn golden brown.
Let the cookies cool on the sheets for a few minutes before transferring them to a wire rack to cool completely.