Make the peanut shortbread: Line a straight-sided 13x9-inch metal baking pan with foil, letting the ends create an overhanging edge for easy removal.

In a medium bowl, stir together the butter, sugar, and salt. Stir in the flour and peanuts to make a stiff dough. Press the mixture evenly into the bottom of the prepared pan. Prick the dough all over with a fork. Refrigerate the pan for 30 minutes (or freeze for 5 to 7 minutes), until the dough is firm.

Meanwhile, position a rack near the center of the oven and heat the oven to 325 degrees F.

Bake the dough for 20 minutes, then decrease the oven temperature to 300 degrees F and bake until the crust is golden-brown all over and completely set, 20 to 25 more minutes. Let the crust cool completely before topping.

Make the peanut butter filling: Put the peanut butter and butter in the bowl of a stand mixer fitted with the paddle attachment and beat on medium speed until smooth, about 1 minute. Add about half of the confectioners' sugar to the mixer along with the vanilla extract and 1 tablespoon hot water. Beat on low speed until combined, then on medium speed until smooth and fluffy, about 1 more minute. Beat in the remaining sugar and mix, about 1 more minute, until the mixture is smooth and thick, like frosting. If the filling seems too stiff, add another 1 tablespoon hot water and beat for another minute.

With a knife or metal offset spatula, spread the filling over the fully cooled crust. The filling may not spread smoothly and evenly, but don't worry; the ganache will cover it.

Make the ganache: Put the chocolate in a small heat proof bowl. In a small saucepan, bring the heavy cream to a boil. Remove from the heat and pour over the chocolate. Let sit for 3 minutes. Stir gently with a rubber spatula until combined and smooth.

Spread the ganache over the peanut-butter filling with a metal offset spatula to coat evenly. Let the bars sit at least 3 hours to allow the ganache to set before cutting (or refrigerate for 1 hour).

Carefully lift the bars from the pan using the foil sides and transfer them to a cutting board. Separate the foil from the bars by sliding a spatula between them. Cut the bars into 1-1/2-inch squares.

Make Ahead: The bars will keep at room temperature for 1 week.

For the best results, measure your flour by weight instead of volume. (1 cup of all-purpose flour equals 4-1/2 ounces) If you don't have a scale, be sure to use the proper technique when filling your measuring cups.