Preheat oven to 350 degrees. In medium bowl, stir together flour, baking soda, and salt.
In large bowl with mixer at medium speed, beat butter and brown sugar until combined. Reduce speed to low and beat in egg until blended. Beat in flour mixture until combined, scraping bowl occasionally with rubber spatula.
Shape dough into two balls; flatten each slightly. Wrap one ball in waxed paper and refrigerate while working with the other half.
On a lightly floured surface with floured rolling pin, roll 1 ball of dough 1/8 inch thick. Cut out as many cookies as possible with cookie cutters, reserving the trimmings to re-roll.
Place cookies on an ungreased cookie sheet, about 1/2 inch apart. Sprinkle with granulated sugar if desired, or bake without sugar and frost when cooled.
Bake until edges begin to brown, about 10 minutes. Transfer to wire rack to cool completely.