In a stand-alone mixer with a paddle attachment, cream the softened butter and sugar together for 2 minutes until light and fluffy.
Add the egg, vanilla, and salt. Mix for 1 minute until everything is well incorporated.
Gradually add the all-purpose flour to the mixture. Mix until the dough comes together and no streaks of flour remain.
Shape the dough into a disc, wrap it in plastic wrap, and chill in the refrigerator for at least 1 hour. This makes rolling out the dough easier.
Preheat the oven to 350°F (175°C). Roll out the chilled dough on a lightly floured surface to about 1/4 inch thickness. Use your favorite cookie cutters to cut out shapes.
Place the cookies on a parchment-lined baking sheet. Bake for 10-11 minutes, or until the tops are no longer shiny. Do not let them brown – they should be pale for the softest texture.
Let the cookies cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely. Once cooled, decorate with icing, sprinkles, or enjoy them as they are!