Line a sheet pan with parchment paper and set aside.
Combine melted butter, peanut butter, granulated sugar, and vanilla extract in a medium bowl and beat together (with a hand mixer or standing mixer) until combined.
Add the powdered sugar and beat again until combined - the mixture will be crumbly.
Use a 1 tablespoon cookie scoop to scoop out about 28 balls of peanut butter mixture.
Roll each scoop between the palms of your hands to form a ball and place each ball on the prepared sheet pan.
Place the sheet pan in the freezer for 30 minutes. After the peanut butter balls are fully chilled, prepare the chocolate coating.
Combine the chocolate chips and shortening in a heatproof bowl. Heat and stir in 30-second increments in the microwave until the chocolate is smooth and melted completely (if there are just a few solid pieces of chocolate left in the bowl, discontinue heating and simply stir until all of the chocolate melts and is smooth).
Using a fork or chocolate dipping tool, dunk peanut butter balls into the chocolate and turn to fully coat them. Tap the excess chocolate off of the ball and place it onto a sheet of parchment paper. You may need to remove balls from the freezer just a few at a time so that they are fully chilled when going into the chocolate. This helps the chocolate harden more quickly.
Allow chocolate to harden. After all of the balls have been dipped, scoop the excess melted chocolate into a plastic baggy or piping bag. Snip a small corner from the bag and drizzle over the chocolate coated peanut butter balls.
Allow drizzle to set and serve immediately.
Store in an airtight container on the counter or in the refrigerator for up to 7 days. Freeze up to 3 months, though discoloration/speckling may occur. Defrost in the refrigerator before serving.
If the chocolate starts to become thick or gloppy, reheat for 15 seconds at a time until it is nice and smooth and thin again for coating.
If it is particularly warm in your house, you can pop the dipped balls back into the refrigerator or freezer to help them set more quickly - sometimes this will affect the sheen of the chocolate coating, but it will not affect the flavor!