Add the flour, baking soda, and salt to a medium bowl, and stir them together.
Add the butter and peanut butter to a large bowl (a stand mixer works best or use a hand mixer) and cream them together until they are totally smooth.
Add in the sugars, and mix them into the butters for about 2 minutes, until light and fluffy.
Add in the eggs, one at a time, until just mixed. Then stir in the vanilla extract.
Add in the flour mixture, and stir them to combine, scraping the bottom and sides of the bowl as needed.
Add in the oats and peanut butter chips and fold them into the dough until combined.
Cover the bowl with plastic wrap and place it in the fridge for 30 minutes to chill.
Preheat the oven to 350 degrees Fahrenheit. Line a cookie sheet or two with parchment paper, or a silicone liner.
Scoop 2 TBS of dough and roll it into a ball. Place the ball onto the prepared baking sheet, about 3 inches apart.
Bake the cookies for 9 to 12 minutes, or until the edges are golden brown and the tops look just set.
Remove the pan from the oven and let the cookies cool on the tray for 10 minutes. Then transfer them to a cooling rack to cool completely.