For the Crust: Preheat oven to 350ºF and adjust oven rack to lower-middle position. Line a 13 by 9-inch pan with aluminum foil, allowing an extra inch or two of foil to hang over edges of pan. In the bowl of a food processor, process crackers until fine crumbs form. Add peanuts to the crumbs and pulse until nuts are coarsely chopped. Add in sugar, salt and butter and pulse a few more times until combined. Pour into prepared pan and, using your fingers or the bottom of a glass, firmly press into an even layer. Bake until set and beginning to brown, about 12 to 14 minutes. Set aside and allow to cool completely.
For the Peanut Butter filling: Place the confectioners' sugar, peanut butter, butter, cream, vanilla, and salt in the bowl of an electric mixer fitted with a paddle attachment. Mix on medium-low speed until smooth and well-mixed, scraping down the bowl with a rubber spatula as you work, about 2 minutes. Switch to wire whisk and whip on medium-high speed until the mixture is lighter in color and a little fuller in volume, 3 to 4 minutes. Pour on top of cooled crust and spread evenly with an offset spatula or butter knife. Chill for at least 20 minutes before topping with chocolate.
For the chocolate topping: Add chocolate chips to a heat-proof bowl. Heat heavy cream in a small saucepan set over medium-low heat until just simmering. Pour hot cream over chips and let sit for 3 minutes. Stir until mixture is smooth. Stir in vanilla extract. Allow chocolate to cool slightly, about 5 minutes, then spread evenly over chilled peanut butter layer. Sprinkle with chopped peanuts. Refrigerate for at least 20 minutes before cutting. Serve chilled, directly from the refrigerator or at cool room temperature.