Lightly grease a 9x13-inch baking pan with butter or non-stick cooking spray. Alternatively, line the pan with parchment or wax paper, leaving an overhang for easy removal.
In a large saucepan, melt the butter over low heat. Once melted, add the mini marshmallows and stir until completely melted and smooth. Remove from heat and stir in the peanut butter until well combined.
Quickly add the Rice Krispies cereal to the melted mixture. Stir gently but thoroughly to coat all the cereal with the marshmallow mixture.
Transfer the mixture into the prepared pan. Press it down firmly using a spatula or your hands (lightly greased to prevent sticking) to ensure an even layer.
In a microwave-safe bowl, combine the chocolate chips and vegetable oil. Microwave in 30-second intervals, stirring in between, until the chocolate is completely melted and smooth.
Pour the melted chocolate over the pressed cereal mixture in the pan. Use a spatula to spread it evenly over the top.
Allow the treats to cool at room temperature for about 30 minutes. Then, refrigerate for at least 1 hour to let the chocolate set and the bars firm up.
Once set, lift the treats out of the pan using the parchment overhang. Place on a cutting board and slice into squares. Serve immediately or store as directed below.