Spray a 9 x 13-inch pan with cooking spray. Preheat your oven to 350 degrees.
Melt the butter in a large glass bowl. Add the brown sugar and peanut butter and whisk until very smooth. Whisk in the eggs and vanilla.
Add the flour, baking soda, and salt to the peanut butter mixture. Stir just until barely combined. Fold in the 1 2/3 cups of chocolate chips.
Press the dough into the bottom of the prepared pan. Drop small dollops of the 1/3 cup peanut butter evenly over the dough; swirl with a knife. Sprinkle the 1/3 cup of chocolate chips over the top.
Bake at 350° for 25-30 minutes, or until the middle is set and the edges are golden brown.
Let the bars cool on a wire rack for at least 30 minutes before cutting into squares.
Notes
If you are using unsalted butter, add an additional 1/4 teaspoon of salt.
Leftover bars can be stored in an airtight container at room temperature for up to a week.