Preheat the oven to 350° and position 2 racks in the lower third. In a medium bowl, whisk together the flour, baking soda, baking powder and salt. In a large bowl, using an electric mixer, beat the butter with the brown sugar and granulated sugar until fluffy. Add the eggs and vanilla and beat at low speed until blended. Add the peanut butter and beat until combined. Beat in the dry ingredients just until incorporated. Beat in the chocolate chunks and peanuts.