Preheat oven to 350°F. Line a square 8x8-inch pan with parchment paper, leaving an overhang on all sides to easily lift the bars out of the pan when cool.
Whisk the flour, baking soda, cornstarch, and salt together in a large bowl.
In a medium bowl, whisk the melted butter, peanut butter, brown sugar, and granulated sugar together until no brown sugar lumps remain and the mixture is smooth. Whisk in the vanilla, egg, egg yolk, and then the milk. The mixture will be thick.
Pour the wet ingredients into the dry ingredients and use a rubber spatula to mix together until combined. The dough will be very soft and thick. Fold in the peanut butter chips. The chips may not stick to the dough because of the melted butter, but do your best to evenly distribute them into the dough.
Transfer the dough to the prepared pan and press it into all four corners of the pan, smoothing out the top into an even layer.
Bake for 32-35 minutes or until lightly browned on the sides. Insert a toothpick into the center of the bars to test for doneness. If it comes out clean, the bars are done. Start checking for doneness around 30 minutes as every oven and baking pan varies and can affect the cook time.
Allow the bars to cool in the pan set on a wire rack for at least an hour. Use the parchment paper to remove the bars from the pan. Cut into 16 squares and serve. Store in an airtight container at room temperature for up to a week.