In a large bowl, beat peanut butter and powdered sugar together until smooth.
Set out the shortbread cookies on a sheet pan lined with parchment paper.
Form balls of peanut butter mixture, then press and flatten them onto the shortbread cookies. Place cookies in freezer while preparing the chocolate chips.
Add chocolate chips to a microwave-safe bowl. Melt in the microwave in 15-second bursts, stirring for 10 seconds between bursts, until smooth and melted.
Dunk cookies in melted chocolate, pull them out with a fork, and tap off excess chocolate.
Place cookies on the parchment-lined sheet pan to set (or refrigerate for quicker setting).
Notes
Note 1: I like Walker's pure butter shortbread cookies, but any will work here. Also read the text above the recipe for other ideas for the bases of these cookies. The Walker shortbread cookies are larger than most cookies, and there are fewer of them (9 per package). If you use a different cookie, you'll have to adjust the toppings (might need more or less of the peanut butter mixture and/or chocolate).