Preheat the oven to 350°F and line two baking sheets with parchment paper or Silpats.
In a medium bowl, whisk together the flour, baking soda and salt. Set the mixture aside.
In the bowl of a stand mixer fitted with the paddle attachment, beat together the butter, sugar and brown sugar until light and fluffy, about 2 minutes. Add the eggs one at a time, beating between each addition, then add the peanut butter and vanilla extract and beat just until combined.
Add the flour mixture to the stand mixer in three additions, beating just until combined, then beat in the chocolate chunks.
Using two spoons or an ice cream scoop, portion out about 1/4-cup amounts of the cookie dough onto the baking sheets, spreading the mounds at least 3 inches apart. Bake the cookies for 18 to 22 minutes until the edges are golden and the centers are barely cooked. Remove the cookies from the oven and allow them to cool on the baking sheets for 5 to 7 minutes before transferring them to a rack to cool completely. (See Kelly's Note.)