Preheat oven to 350° F. Line a baking sheet with parchment paper.
Beat butter, brown sugar and white sugar on high until fluffy, about 2 minutes. Add in egg and vanilla and beat until lightened and fluffy, about 1 minute. Add peanut butter and beat on medium speed until well combined. Add flour, baking soda and salt and beat on medium low speed just until combined, no longer.
Roll dough into large balls, about 2- 2 ½ Tablespoons in size. Place on cookie sheet, leaving them plenty of room to spread, only 12 per baking sheet. Flatten slightly (see photo above) using your fingers or the palm of your hand. Bake for 10 minutes. They are done as soon as the tops are matte and the edges are set. Bang pan on the oven a few times to help them crinkle. Allow to cool on the baking sheet at least 8 minutes before removing. Enjoy!
Video
Notes
Make sure your butter isn't overly softened or the cookies won't have the perfect texture. The butter should be soft enough you can make a dent in it when you press on it with your finger, but should not be mushy at all.
You can use a fork to flatten these for a more stereotypical peanut butter cookie appearance, but I love the way they look all crinkled.
Sometimes I'll roll the cookies in granulated sugar before baking. This can add a special touch.
The most important thing you can do for the texture of these cookies is do NOT over bake!! Peanut butter cookies dry out very quickly, and even 2 minutes extra in the oven will make them crumbly and dry instead of soft and oh so chewy.