Line muffin pan with cupcake liners and set aside.
In a medium-sized mixing bowl, combine peanut butter, powdered sugar, vanilla extract, and salt and stir to combine. Should form a soft dough rather quickly. Set aside.
Place chocolate chips and 2 tbs of oil in a glass bowl or measuring cup and melt in a pan of hot water (double boiler method) or in the microwave on 30 second intervals. Stir regularly so that chocolate doesn't burn.
Pour chocolate into cupcake liners so it's about 1/4 inch thick (about 1 tbs per liner). Place in refrigerator for 5 minutes to harden.
While chocolate is in the refrigerator, take about 1 tbs of the peanut butter mixture and roll it into a ball. Flatten it into a patty and set aside. These will become the center of your peanut butter cups, so make sure they are smaller than the chocolate base.
Once the chocolate in the muffin pan has hardened a bit, remove it from the refrigerator and place one peanut butter disc in each liner. If your bowl of chocolate has hardened again, place back in double boiler or microwave so that it is pourable before moving on to the next step.
Pour or spoon out 1-2 tbs more of chocolate over the peanut butter discs so that they are fully covered and the top is flat.
Place in the refrigerator for at least 30 minutes to harden before removing from the muffin pan and the liners. Store in an airtight container in the refrigerator for 1-2 weeks (if they last that long).
Notes
You could easily make these in a mini muffin pan for a smaller treat. Just make sure to make the peanut butter discs smaller than the bottom of the chocolate and all will be well.
You may need to add more powdered sugar depending on the brand of peanut butter you choose. Because natural peanut butter is a little thinner than their no-stir counterparts, they will probably require a bit more powdered sugar than listed. I would suggest adding it in 1 tbs at a time until you hit the desired consistency.