Preheat oven to 350°F. Lightly grease a large cookie sheet; set aside.
In a large bowl, combine eggs, egg whites, peanut butter, and vanilla. Beat with an electric mixer on medium speed until smooth. Add brown sugar, baking powder, baking soda, and salt. Beat just until combined, scraping side of bowl occasionally. Beat in as much of the flour as you can with the mixer. Using a wooden spoon, stir in any remaining flour, the peanuts, and chocolate pieces.
Turn dough out onto a lightly floured surface; divide in half. Using well-floured hands, shape each portion into an 11-inch-long loaf. Place loaves about 4 inches apart on the prepared cookie sheet; flatten loaves slightly until about 2-1/2 inches wide.
Bake in the preheated oven about 25 minutes or until lightly browned and a toothpick inserted near the centers comes out clean. Cool on cookie sheet on a wire rack for 15 minutes.
Reduce oven temperature to 300° F. Transfer baked loaves to a cutting board. Using a serrated knife, cut each loaf diagonally into 3/4-inch-thick slices. Place slices on ungreased cookie sheets. Bake for 8 minutes. Turn slices over; bake about 8 minutes more or until crisp and golden brown. Transfer cookies to wire racks; let cool.