Preheat oven to 350°F (175°C). In a large mixing bowl, beat butter and sugars until light and fluffy. Mix in the peanut butter. Add the eggs and vanilla and mix well. With mixer on low speed, mix in the flour, baking soda and salt until combined.
Roll tablespoon sized (cookie scoop sized) dough into balls. Coat the balls in sugar and place on an ungreased baking sheet. Press the dough balls down with the tines of a fork and bake the cookies for 8-9 minutes.
Remove from the oven, allow the cookies to set for a couple of minutes and then transfer them to wire racks to cool completely. Store in an airtight container at room temperature for up to one week or freeze for up to two months.