In a microwave-safe bowl, combine the creamy peanut butter and unsalted butter. Microwave in 30-second intervals, stirring between each, until the mixture is smooth and well combined.
Stir in the powdered sugar, vanilla extract, and salt until the mixture forms a dough-like consistency.
Line a muffin tin with 12 paper cupcake liners. Take a small portion of the peanut butter mixture and flatten it into a disc, then place it in the bottom of each cupcake liner. Ensure it covers the entire bottom evenly.
In a microwave-safe bowl, combine the chocolate chips and vegetable oil. Microwave in 30-second intervals, stirring between each, until the chocolate is completely melted and smooth.
Spoon the melted chocolate over the peanut butter filling in each cup, ensuring the peanut butter is completely covered. Use the back of a spoon to smooth out the chocolate on top.
Place the muffin tin in the refrigerator and let the peanut butter cups chill for at least 1-2 hours, or until the chocolate is firm.
Once the peanut butter cups have hardened, remove them from the muffin tin and peel off the paper cupcake liners. Your homemade peanut butter cups are now ready to be enjoyed!