Cream the butter and peanut butter together until thoroughly combined. Beat in the vanilla.
Sift the sugar, flour and salt together and then add to the butter mixture. Mix until the dough comes together and is no longer dry and crumbly. A stand mixer helps with this job.
Add the chocolate chips in towards the end of mixing and distribute evenly.
Turn the dough out onto a board and continue to work it with your hands until it comes together like a pie dough. Divide it in two equal parts, and shape them into flat disks. Wrap tightly in plastic and refrigerate for about an hour.
Roll out the chilled dough on a lightly floured surface to your desired thickness. I rolled mine to about 1/4-1/3 inch.
Bake on a parchment lined baking sheet for about 13-15 minutes. They will soft and white even when done, but will firm up as they cool.
Let the cookies rest on the hot cookie sheet for a minute or two, and then transfer carefully to a cooling rack.