Preheat the oven to 350 degrees and line two baking sheets with parchment paper or silicone baking mats.
In a large bowl or the bowl of a stand mixer, cream together the butter and the peanut butter until well combined and smooth, about 2 minutes. Add the sugars and beat together an additional 1-2 minutes. Scrape the sides of the bowl and add the egg and vanilla. Beat briefly just to combine. In a separate smaller bowl, stir together the flour, oats, baking soda, and salt. Add to the butter mixture and beat just until combined. Add the chocolate and stir together.
Scoop 3 tablespoon sized mounds of dough (I use a large cookie scoop) 2″ apart on the baking sheet. Roll in the chopped peanuts, if desired. Bake in the preheated oven for about 12 minutes, or just until the edges have set and the top is beginning to crack. The center may seem underdone. Allow to cool on a cooling rack prior to eating. Enjoy within 2 days or freeze up to 2 months.