In a medium bowl, combine the peanut butter, unsalted butter, and brown sugar until smooth.
Gradually add in the powdered sugar and mix until fully incorporated. Set this mixture aside.
Melt the chocolate chips and vegetable oil in a microwave-safe bowl in 30-second intervals, stirring between each interval until smooth and completely melted.
Spoon a small amount of the melted chocolate mixture into the bottom of each cupcake liner, filling about 1/3 of each liner.
Place the liners in the refrigerator for about 10 minutes to set.
Remove liners from the refrigerator, add a spoonful of the peanut butter mixture on top of the set chocolate, and flatten it slightly.
Cover the peanut butter layer with melted chocolate until each liner is almost full.
Refrigerate the liners for another 20 minutes or until the chocolate is completely set.
Remove Peanut Butter Cups from the liners and enjoy!