In a large bowl, cream together the egg, brown sugar, peanut butter, butter, and vanilla extract. A mixer is best. Pause every so often to scrape down the sides of the bowl, but continue mixing until the dough is light and fluffy, about 5 minutes.
Add the flour, baking soda, and salt until just incorporated. Add the peanut butter and chocolate chips.
Place two large strips of plastic wrap on the counter. Divide the dough in half, compress it to be stackable, and completely wrap each big disc. Stash it in the fridge for a couple of hours or up to five days. (Chilling the dough makes the end result thick and pillowy! Don't skip this.)
Preheat the oven at 350-degrees. Line a baking sheet with a silicon mat or parchment paper. Use a tablespoon scoop to dole out the dough. Compress each ball of dough to a thick oval; this is important because the dough won't spread much as it bakes.
Bake for 10-12 minutes, until the edges have just set. Allow the cookies to rest on the baking sheet another 10 minutes; they will firm up during this time. Transfer them to a rack to finish cooling, and start the next batch.
Cookies will keep at least five days in a sealed container at room temperature.