Preheat the oven to 350°F. Line an 8 by 8-inch metal baking pan with parchment or foil.

In a saucepan over medium heat, melt the butter. Add the brown sugar, stirring until smooth. Remove from the heat and stir in the peanut butter. Allow to cool.

In a large mixing bowl, combine the flour, baking powder, baking soda and salt.

Once the butter mixture is cool, add the eggs and yolk, one at a time, stirring until well combined. Stir in the vanilla extract. Pour the mixture into the prepared dry ingredients, and stir to create a very thick dough-like batter. Fold in 3/4 the chocolate chunks, reserving the rest for sprinkling on top.

Transfer the batter to the prepared pan, spreading evenly to the edges. Sprinkle with the remaining chocolate chunks, lightly pressing them into the batter.

Bake for 30 minutes, or until the top is golden and the edges are slightly browned. Allow to cool in the pan. Use the parchment to remove the bars before cutting into squares and serving. Store in an airtight container at room temperature for up to 3 days.