Preheat the oven to 350° F.
Using a paddle attachment on your electric mixer, place the butter and sugar and mix until fluffy and combined.
Add the egg and vanilla and mix together
In a medium bowl, add the flour a salt and mix. Add to the butter-sugar mixture and mix on slow speed until the dough comes together.
On a floured surface, place the ball of dough and shape into a flat disk. Wrap and chill in the refrigerator for about half an hour.
Once cooled, roll the dough on a floured surface to 1/4 inches thick, then use your cookie cutters. Place the cookies on an ungreased baking sheet and bake for 12 to 15 minutes or until the edges begin to turn brown.
Remove from the oven and cool to room temperature. Once cooled, you can frost with a buttercream frosting. (Use the recipe on the box of powdered sugar). If you wish, decorate with colored sugar or other cookie sprinkles.