In a large bowl, using a handheld or stand mixer, cream butter (including peanut butter) and sugars together until light and fluffy.
Add egg, and then the vanilla. Slowly mix in the baking soda and flour. Do not overmix.
Chill dough for at least an hour.
When you are ready to bake preheat your oven to 350 degrees.
Remove dough from fridge and roll into balls. I make little golf balls around 2 inches in diameter. You can make them as big or as small as you would like.
Spread a thin layer of granulated or raw sugar on a plate and roll each dough ball to evenly coat (if desired). I usually do this and my husband always skips this step.
These cookies spread so be sure to space them out on your cookie sheet. I usually use parchment paper on an ungreased baking sheet.
Bake for 20 minutes, on your middle rack, if your cookie balls are about 2 inches wide. Leave cookies on your baking sheet for 5-10 minutes and then transfer to a rack to cool.
No matter what size you decide to make your cookie balls, you will know when they are done because the tops will crack and you might notice a little brown around the edges. That is time to take them out of the oven. These cookies will look undone, but will firm up as they cool. Do not over bake them.
These cookies will stay fresh and soft in an airtight container for up to 5 or 6 days and freeze beautifully.