In a bowl, with an electric mixer on medium speed, beat butter, granulated sugar, brown sugar, and peanut butter until well blended. Beat in eggs and vanilla until smooth, scraping down sides of bowl as needed.
In another bowl, mix flour, cocoa powder, baking powder, and salt. Stir or beat into butter mixture until well incorporated. Stir in chocolate chips, oats, and peanuts.
Drop dough in rounded 2-tablespoon portions, 3 inches apart, onto buttered or cooking parchment-lined 12- by 15-inch baking sheets. With a lightly floured fork, flatten slightly into 2 1/2-inch rounds about 1/2 inch thick.
Bake in a 350° oven until cookies are golden and tops feel set when lightly pressed, 12 to 14 minutes (they will feel underdone but will firm up as they cool); if baking more than one pan at a time, switch pan positions halfway through baking.
Let stand 5 minutes on sheets, then, with a wide spatula, transfer cookies to racks to cool. If hot cookies start to break, slide a thin spatula under them to release; let stand on pan to firm up, 2 to 5 minutes, then transfer to racks to cool completely.
Note: Nutritional analysis is per cookie.