Combine the flour, baking soda and salt in a medium bowl. In a large bowl beat the butter, peanut butter, white sugar and brown sugar until well combined. Add the egg and beat until creamy and fluffy. Slowly add the dry ingredients to the butter mixture then beat until well combined. Divide into three balls and wrap in plastic wrap then refrigerate for 3 hours.
On a lightly floured surface roll out the dough and cut with a cookie cutter. Transfer to a parchment lined cookie sheet and bake until lightly browned 8 to 10 minutes. Cool on a baking rack then decorate if desired.