Whisk the flour, salt, and sugar together. Cut in the cold butter until you have pea-sized pieces. Add cold water a tablespoon at a time, tossing gently, until the dough is crumbly and shaggy. Turn it out, press it together with the heel of your hand until it just comes together, divide, press into disks, wrap, and chill for 2 hours or overnight.

Roll one disk to ⅛ inch thick between two sheets of parchment while it is still cool but pliable. Chill flat on a baking sheet for at least 30 minutes, until firm.

Lay the chilled round into a 9-inch pie dish. Lift the edges to settle the dough without stretching it. Press the sides to fit, roll the overhang under, press to seal, and flute the edge. Chill 10 to 30 minutes, until firm.

Preheat the oven to 350°F convection or 375°F conventional. Line the chilled shell with crumpled parchment and fill with pie weights. Bake 15 to 20 minutes, until the sides and bottom look matte and the edges just begin to brown. Remove the weights and parchment.

For the caramel, combine the cream, butter, vanilla, and salt in a small pot and bring just to a boil. Set aside. In a separate heavy-bottomed pot over medium-high heat, melt the sugar in stages, stirring to break up clumps. Once fully melted, stop stirring and swirl until deep amber. Remove from heat and slowly whisk in the hot cream mixture. Pour into a heat-safe bowl and cool to room temperature.

Preheat the oven to 325°F convection. In a bowl set over a bain marie, melt the butter, dark chocolate, and cocoa powder together, stirring until smooth. Reserve warm.

In a separate bowl, whisk together the granulated sugar, light brown sugar, eggs, and egg yolks until smooth and slightly lightened. Whisk in the warm chocolate mixture all at once, then whisk in the peanut butter until smooth.

Scatter about ⅔ cup of the chopped peanuts over the bottom of the parbaked shell. Pour the salted caramel over the peanuts and spread evenly. Pour the chocolate peanut butter filling over the caramel and smooth the top. Sprinkle the remaining chopped peanuts around the edges.

Bake at 325°F convection for 50 to 55 minutes, until the edges are set and the center has a slight jiggle. Cool completely before slicing. For the best texture and cleanest slices, chill in the refrigerator for at least 3 hours or freeze for 1 to 2 hours before cutting.