Line your 9x9 inch pan with parchment paper, leaving some overhang on the sides for easy removal.
In a microwave-safe bowl, combine the chunky peanut butter and melted butter. Microwave in 30-second bursts, stirring each time, until the mixture is smooth, creamy, and fragrant—about 1 to 2 minutes.
Add the sifted powdered sugar to the peanut butter mixture and stir well until fully incorporated. The mixture should become thick and slightly sticky.
Pour the peanut butter mixture into the prepared pan. Use a spatula to spread it evenly across the bottom, pressing gently to create a smooth, rustic surface with some uneven edges for that homemade charm.
Place the pan in the fridge and chill for about 20 to 30 minutes, or until the layer is firm to the touch.
Meanwhile, melt the semi-sweet chocolate chips in a microwave-safe bowl in 20-second intervals, stirring each time, until they are glossy and smooth. Be careful not to overheat, smelling for a rich cocoa aroma.
Remove the pan from the fridge once the peanut butter layer is firm. Pour the melted chocolate over the top, tilting the pan to spread it evenly with a spatula.
Return the pan to the fridge and chill for at least an hour, or until the chocolate layer is fully set and shiny.
Once set, let the bars sit at room temperature for 5 minutes to soften slightly, then use the parchment overhang to lift the entire slab out of the pan.
Use a sharp knife to cut into squares or rectangles, wiping the blade between slices for clean edges. Serve immediately or store in an airtight container in the fridge for up to a week.