Preheat your oven to 325℉ and prep a 9x9 square baking pan with parchment paper and greased.
Using either a stand or hand mixer, beat together the butter and sugar until pale - about 3 minutes. Add in the vanilla, salt, and AP flour and mix to combine. Spoon into the baking dish and spread out in an even layer on the bottom. Bake for 30 minutes until golden brown on the edges. Allow to come to room temp before adding next layer on top.
For the peanut butter layer, melt the butter in a microwave safe bowl, then add the PB, confectioners sugar and salt and mix to combine. Spread over the shortbread mixture (once the shortbread has cooled!). Then place in the fridge while you prep the chocolate layer.
For the chocolate layer, in a microwave safe bowl, melt the chocolate chips with the heavy cream in 2x increments of :30 - stirring between. It won't look completely melted after the 1 minute, but keep stirring and it will all melt together. Then mix in the Rice Krispies, salt, and vanilla. Add as the top layer to the bars, spreading evenly.
Refrigerate for at least 2 hours, up to 5 days.
Notes
* yield is highly dependent on how you cut it! I cut mine in triangles, and got 12. You could do squares and get 9 large squares, 12 smaller squares, or even 16 teeny squares.