Heat the oven to 350°F and line baking sheets with parchment.
Beat the peanut butter, softened butter, granulated sugar, and brown sugar until smooth and creamy.
Beat in the eggs one at a time, then mix in the vanilla.
Whisk the flour, baking soda, and salt separately. Add them to the wet mixture and stir just until no dry streaks remain.
Scoop rounded tablespoons of dough onto the prepared sheets, leaving space between each cookie.
Bake for 9 to 11 minutes, until the edges are set and the centers still look slightly soft.
Cool on the baking sheet for 5 minutes, then transfer to a rack to cool completely.