Preheat oven to 350°F (175°C). Line a 9×9-inch baking pan with aluminum foil and spray the foil with cooking spray; set pan aside.
In the bowl of a stand mixer fitted with the paddle attachment (or in a large bowl with an electric mixer), add the 21-ounce cake mix, 1 large egg, 1/2 cup very well softened unsalted butter, and 1 teaspoon vanilla extract. Mix on medium speed until combined, stopping to scrape down the sides as needed.
The dough should be very thick and come together as a single, softball-like mass that sticks to the paddle. If it does not come together, add up to 3 tablespoons water, 1 tablespoon at a time, mixing after each addition, until the dough forms that mass. Do not add more than 3 tablespoons.
Transfer approximately half of the dough into the prepared pan. Press it evenly into the bottom of the pan with a spatula or your fingertips to form a flat crust.
Evenly sprinkle 1 cup semi-sweet chocolate chips over the crust.
In a medium bowl, whisk together half of the 14-ounce can of sweetened condensed milk and 1/2 heaping cup creamy peanut butter until smooth and fully combined.
Spoon or pour the peanut butter–sweetened condensed milk mixture over the chocolate chips, keeping a 1/2-inch bare margin from the edges. Smooth lightly with a spatula as needed.
With the remaining dough, form small ~1-inch pieces or balls and drop them evenly over the top of the filling. Press gently to compact and seal; full coverage is not necessary.
Bake on the middle rack for 25–27 minutes, or until the top is just set and not jiggly. (A toothpick test will appear wet because the interior is intentionally gooey.)
Immediately after removing the pan from the oven, use the blunt end of a wooden spoon to poke about 25 holes roughly 1/2-inch deep across the surface.
Evenly drizzle the remaining sweetened condensed milk from the can over the bars, aiming to fill the holes as best you can.
Allow the bars to cool uncovered at room temperature for at least 3 hours before serving (overnight is best so the sweetened condensed milk soaks in more). Store airtight at room temperature for up to 1 week.