Preheat oven to 350°F (175°C). Grease and flour a 9x13 inch baking pan.
In a large bowl, cream together softened butter and packed brown sugar until light and fluffy. Stir in vanilla extract.
Beat in the eggs one at a time until fully incorporated.
In a separate bowl, whisk together all-purpose flour, baking soda, and kosher salt.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Do not overmix.
Stir in the semi-sweet chocolate chips.
Press half of the cookie dough evenly into the bottom of the prepared baking pan. Reserve the remaining dough for the topping.
Bake for 15 minutes, or until lightly golden.
Remove the pan from the oven and carefully spread the melted peanut butter evenly over the baked cookie layer.
Crumble or flatten small pieces of the remaining cookie dough and place them over the peanut butter layer. It's okay if some peanut butter shows through.
Return to the oven and bake for an additional 20-23 minutes, or until the cookie topping is golden brown and the peanut butter is bubbling.
Let the bars cool completely in the pan on a wire rack before cutting into squares.
Notes
For extra flair, you can drizzle melted chocolate over the cooled bars.