Cream together the butter and sugars.
Add egg and vanilla, and mix well.
In a small bowl, combine flour, baking soda, and salt.
Add dry ingredients to the wet ingredient.
Mix until thoroughly combined, and chill dough in the refrigerator for at least 2 hours.
Preheat oven to 350 degrees. Roll out the cookie dough to 1/4" thick, and cut with cookie cutters.
Bake on a lined cookie sheet for 7-10 minutes or until the cookies are lightly golden.