Preheat the oven to 350°F. Line a baking sheet with parchment paper. You can use 2-3 baking sheets, or bake on one baking sheet in a few batches.
In a mixing bowl, mix together smooth peanut butter and softened butter using an electric mixer or a stand mixer with a paddle attachment. Beat until combined and smooth. Then, add packed brown sugar and granulated sugar. Beat for 2-3 minutes or until light and fluffy. Mix in eggs and vanilla extract. Then, add all-purpose flour, baking soda, and salt. Beat until combined and flour just disappears. Don't over mix the batter.
Shape the batter into small balls. Place them on the prepared baking sheet about 2 inches apart. Then, flatten the cookies with a fork. Bake in the preheated oven for 7-10 minutes or until golden. Remove the baking sheet from the oven and let the peanut butter cookies cool completely.