Preheat the oven to 350°F (177°C). Line an 8x8-inch baking pan with aluminum foil and spray the foil with cooking spray; set aside.
In a large microwave-safe bowl, melt the 1/2 cup (1 stick) melted unsalted butter in the microwave for about 1 minute.
Let the butter cool briefly so it doesn’t cook the egg, then whisk in the egg, 1/2 cup packed light brown sugar, and 2 teaspoons vanilla until smooth.
Stir in 1 1/2 cups all-purpose flour and a pinch of salt (optional) until just combined; do not overmix. The batter will be thick.
Turn the batter into the prepared pan, smoothing it lightly with a spatula and pressing it into the corners.
Evenly sprinkle the chopped graham crackers (from 4 crackers) over the batter, then sprinkle 1 cup semi-sweet chocolate chips on top.
In a large mixing bowl, whisk together the 14-ounce can of sweetened condensed milk and 1/2 cup creamy peanut butter until smooth and combined.
Slowly and evenly pour the peanut butter–condensed milk mixture over the bars, smoothing lightly with a spatula and pushing any exposed graham pieces down so they are coated.
Bake for 28 to 31 minutes, until the top is set and slightly golden but not jiggly. Watch closely near the end to avoid burning.
Cool the bars in the pan for at least 3 hours (overnight is best) before lifting them from the foil and slicing into 9 generous pieces.