Preheat the oven to 350°F. Line an 8x8-inch baking pan with aluminum foil, leaving an overhang on two sides to lift the bars out later; set the pan aside.

In a large microwave-safe bowl, melt ½ cup unsalted butter on high for about 1 minute. Let the melted butter cool 1–2 minutes so it is warm but not hot.

Reserve about 1 teaspoon of the cooled melted butter and use it to lightly grease the foil-lined pan. (Use the remaining melted butter in the batter.)

To the bowl with the remaining melted butter, add ⅓ heaping cup peanut butter, 1 large egg, 1 cup light brown sugar (packed), and 1 tablespoon vanilla extract. Whisk until the mixture is smooth and uniform.

Add 1 cup all-purpose flour and ½ teaspoon salt to the wet mixture. Stir with a spatula or spoon just until combined — do not overmix.

Stir in 1 cup semi-sweet chocolate chips until evenly distributed.

Pour the batter into the prepared pan and smooth the top lightly with a spatula. Sprinkle the remaining 2 tablespoons chocolate chips evenly over the top and gently press them into the batter.

Bake on the center oven rack for 20–25 minutes, or until a toothpick inserted into the center comes out clean or with a few moist crumbs (no wet batter).

Remove the pan from the oven and let the bars cool in the pan on a wire rack for at least 30 minutes. Use the foil overhang to lift the bars from the pan, then slice and serve.

Store bars airtight at room temperature for up to 1 week, or freeze for up to 6 months.