Preheat the oven to 350°F.
In the bowl of an electric mixer fitted with the paddle attachment, cream the butter, peanut butter, and the sugars for several minutes, starting on low and slowly increasing the speed to medium. Scrape down the sides of the bowl with a spatula.
Add the egg, and beat until it is incorporated, then the vanilla, scraping down the sides of the bowl as needed.
In a separate bowl, combine the baking soda and salt. For chewy/softer/thin cookies, add 125 grams of flour. For thicker chewy cookies, add 188 grams of flour. Whisk the dry ingredients together then add them to the mixer bowl. Beat until combined.
Scoop the cookie dough with a cookie scoop onto parchment-lined cookie sheets, press with a lightly-floured fork to make a criss-cross pattern, and then bake for 10–12 minutes for chewy cookies or for 13–15 minutes for crispier cookies.
Let cool several minutes before transferring to a wire rack to cool completely.