Preheat oven to 350°F. Line a 9x9” pan with foil and spray with cooking spray.
Cream butter and 1/3 cup powdered sugar in the bowl of a stand mixer (or using a hand mixer). Add 1 teaspoon vanilla and mix, scraping the bowl a few times to make sure that the butter and powdered sugar are completely incorporated. Mix in salt and flour until combined. It will take a few moments to turn from crumbly into an actual dough. Just keep mixing until it does.
Press dough into the prepared pan, like a crust.
Bake for 14-18 minutes, until the shortbread is no longer shiny or translucent. It won’t brown very much, if at all. Let cool completely before the next step.
Mix peanut butter, 1/2 cup powdered sugar, and 1 teaspoon vanilla with a hand mixer. Spread evenly over the top of the cooled shortbread.
Melt chocolate chips and shortening in a microwave safe bowl. (Heat on high in 30 second increments, stirring between each, until melted and smooth.) Spread over the top of the peanut butter layer.
Important: it was cold in my house when I made these bars. I let them set and the chocolate harden on the counter. If you must chill them to set the chocolate, make sure you let them come up to room temperature before cutting so that the chocolate doesn’t break. The peanut butter is smooth and does not harden, so if the chocolate is too hard the peanut butter layer will smoosh out while cutting. Letting the bars harden overnight on the counter shouldn’t be a problem, unless it’s summer and very warm in your house