In a standing mixer on medium speed, beat butter, peanut butter, and sugars until light and fluffy, about 2 minutes. Beat in eggs, then vanilla extract.
In a separate bowl, whisk together flour, oats, baking soda and salt. Add to peanut butter mixture with mixer speed running on low. Remove bowl from stand and stir in chopped chocolate. Chill 1 hour before baking (or up to 48 hours).
Preheat oven to 375ºF. Scoop by tablespoonfuls onto parchment-lined baking sheet about 3 inches apart (cookies will spread quite a bit), rolling into smooth balls between your palms for perfect circles. Bake 8-10 minutes, or until edges are golden brown and centres are still pale and slightly undercooked. Cool on wire racks.