In a large bowl, using a hand-held mixer or stand mixer with paddle attachment, cream the butter and sugars together on medium speed. Mix in the peanut butter, egg, and vanilla (in that order). Scrape down the sides as needed. Slowly mix in the baking soda and flour. Do not overmix. Chill the dough for at least 30 minutes.

Preheat oven to 350 degrees. Roll about 1.5 Tablespoons of dough into a ball. Place onto ungreased cookie sheet or silicone baking mat. Bake for 8-9 minutes. Cookies will be soft and may appear undone. They will firm up as they cool.

Allow to cool completely on a wire rack. Cookies stay fresh in an air-tight container for up to 1 week.