In a large mixing bowl, combine the flour, baking soda, and salt.
In an electric mixer, mix the butter, brown sugar, and granulated sugar until well combined.
Add the peanut butter and continue mixing until well combined, stopping to scrape down the sides of the bowl as needed.
Mix in the egg and vanilla extract until fully combined. Slowly add in the dry ingredients and mix until just combined.
Scoop two tablespoons of dough to form each cookie. Roll the scoops into balls and place on lined cookie sheets. Press down on each ball of dough with a fork in a criss-cross pattern to form the cookies. Leave a bit of space between each one.
Bake for 10-12 minutes or until the tops are set. Remove from the oven and allow to cool on the baking sheet for 5-10 minutes, then transfer to a wire rack for cooling.
