Have ready a large baking sheet lined with wax or parchment paper.
Cream together the confectioners sugar, peanut butter, butter and vanilla.
Roll the balls:
Use your hands to roll 1½-inch balls from this mixture, placing them onto the prepared baking sheet. (You can also use a tablespoon-sized cookie scoop, and then roll the ball quickly in your hands to smooth it.)
Refrigerate the balls for 3-4 hours until they are very firm.
Melt the chocolate:
In the top of a double-boiler, heat and stir the chocolate and the vegetable shortening until they're melted and smooth.
Have another sheet of wax or parchment paper ready on a baking sheet where you will place the chocolate-coated balls.
Dip the peanut butter balls:
Spear a chilled peanut butter ball with a toothpick, or use a candy dipping tool or place it on the tines of a fork.
Lower it into the melted chocolate. Coat it thoroughly, using a spoon if necessary. to get the entire surface covered.
Place the ball on the wax paper. Repeat these steps with all of the peanut butter balls.
Allow them to cool for 1-2 hours until the chocolate is set.
Store:
Store the balls in an airtight container at room temperature for 5 days—if by some remarkable chance they do not all get eaten in the first 24 hours!
You can also store the peanut butter balls in the fridge for up to one week.
To store them in the freezer, place them in a single layer in a freezer-proof resealable bag with all the air pressed out. They'll keep for up to 3 months.
Notes
Tips:
Use semisweet baking chocolate for the best texture when the chocolate is melted. Use a good quality like Ghirardelli or Callebaut if possible.
I don't recommend using chocolate chips. They're made with stabilizers that prevent the chocolate from melting as smoothly as baking chocolate.
I like semisweet chocolate as a coating but dark chocolate would also be delicious. You can also try coating the peanut butter balls with white or milk chocolates—just keep in mind that they'll be super sweet!