In a large bowl with an electric mixer (a paddle attachment on a stand mixer works best for this recipe), beat peanut butter and butter until smooth.
Add sugars and beat on high speed until light and fluffy - 2-3 minutes.
Add eggs and vanilla and beat on low speed until combined.
Add flour (fluffed and levelled!), baking soda and salt and beat on low speed just until cookie dough comes together.
Preheat oven to 350 degrees F and line 3 baking sheets with parchment paper.
Roll into 1" balls and place 2" apart on baking sheets.
Press down slightly with fork.
Bake for 8-10 minutes, just until set (a slight glossy sheen in the very center is okay). Remove and let cool on baking sheets before moving to an air tight container to store.