In the mixing bowl with browned butter, add the peanut butter, white sugar, brown sugar, vanilla, salt, baking powder, and baking soda. Mix until batter is well combined, about 3 minutes.
Use an ice cream scoop to place golf-ball sized portions of your cookie dough onto ungreased aluminum baking sheets, with about 2 inches between each of them. Bake for 13-16 minutes.