Preheat oven to 350 degrees. Line a baking sheet with parchment paper.
In a standing mixer or hand blender, cream butter, peanut butter and sugars together for about a few minutes until light and fluffy.
Add egg and vanilla, mix until combined. Add flour salt and baking soda and continue mixing until just incorporated, do not overmix. If you have time, chill dough for at least 30 minutes.
Roll dough into about 1-inch balls and arrange onto a prepared baking sheet, spacing about 2 inches apart. Dip a fork in flour and use the back to gently flatten the cookie and make a criss-cross pattern.
Bake for 12-14 minutes until just firm around the edges and lightly golden. Leave on a baking sheet for a few minutes before transferring to a cooling rack where the cookies will continue to firm up.