Line a nine-inch square pan with aluminum foil by first flipping the pan upside down on the countertop. Press a sheet of aluminum foil around the pan and gently lift it off of the pan. Flip the pan right side up and set the molded piece of aluminum foil into the bottom of the pan and fold any excess around the pan. Set this aside.
Put the graham crackers into a heavy-duty quart-sized zip-top baggie, press out as much air as you can, and seal it up. Use a rolling pin or a meat mallet to crush the graham crackers into coarse crumbs. You want to crush them so that there are no large chunks of graham crackers remaining. Set the baggie of graham cracker crumbs aside until needed.
Using a microwave-safe bowl, put the butter in it and microwave it for about thirty seconds. Stir the butter and, if it is not completely melted, put it back in the microwave for ten to fifteen seconds at a time.
Use a wire whisk to blend 1 cup of the peanut butter with the melted butter. Using a wooden spoon, stir in the graham crackers and the powdered sugar. Stir until everything is fully blended.
Press this mixture into the bottom of the foil-lined pan, spreading it into an even layer, and using a rubber spatula to scrape out the bowl. Put this into the fridge while you move on to making the chocolate topping.
Use a paper towel to wipe out the residue in the mixing bowl. Put the chocolate chips and the remaining ¼ cup of peanut butter in the bottom of the mixing bowl. Microwave this for about thirty seconds.
Stir with a rubber spatula. If the chocolate chips are not melted, return them to the microwave for another twenty seconds. Stir again. When the chocolate chips are melted, you should stir the mixture until it is smooth and creamy.
Take the reserved peanut butter bottom layer out of the refrigerator, and scrape the chocolate out of the bowl and onto the top of it. Smooth it gently into an even layer.
Put the pan into the refrigerator uncovered for two hours. Remove the pan from the refrigerator and lift the peanut butter and chocolate dessert bars out of the pan onto a cutting board with aluminum foil. Peel the foil from the large chunk of bars and cut them into one-inch squares. Store the bars in a tightly sealed container in the refrigerator for up to two weeks.