Roast and caramelize the nuts:
Preheat the oven to 350 F. Line the bottom of a sheet pan with parchment paper. Spread the peanuts on the prepared pan in a single layer. Roast the nuts until they are a medium brown, about 15 minutes.
While the nuts are roasting, put a piece of parchment paper or a nonstick baking liner on a work surface. Measure the sugar and butter and put both of them next to the stove.
As soon as the nuts are roasted, place a medium, heavy-bottomed pot over medium-high heat. Use an unlined copper pot if you have one. When the pot is hot — test it by flicking a drop of water into the pan; it should sizzle and dance across the bottom — immediately add the hot nuts and the sugar. Cook, stirring constantly with a wooden spoon, until the sugar liquefies and coats the nuts. If they start to smoke, reduce the heat. When only a few specks of sugar remain unmelted, remove from the heat. Sprinkle the salt over the nuts and add the butter. Stir until the nuts glisten and start to separate from one another.
Scrape the nuts onto the parchment paper or baking liner and spread them apart. Let the nuts cool completely, and then break up the larger pieces. The pieces don’t have to be uniform.
Store the nuts in a zippered plastic bag at room temperature if you are not making the bark immediately.
Make the bark:
Line the bottom of an 8-by-12-inch sheet pan with parchment paper. Stir the tempered chocolate and peanut butter together in a medium bowl.
Pour the chocolate into the prepared pan. Spread it evenly with a small offset spatula. Tap the pan on a work surface to even the top.
Sprinkle the caramelized nuts over the chocolate. Tap the pan again to settle the nuts into the chocolate. When the chocolate loses its sheen and starts to set, after about 15 minutes, cut the bark with a sharp knife into 2-inch squares or other fanciful shapes of your choice. Leave the bark at room temperature until it is completely set, about 1 hour, and then separate the pieces.
Store in a cool, dry place, not in the refrigerator.