1Heat the oven to 350°F and arrange a rack in the middle. Butter an 8-by-8-inch glass baking dish and set aside. Combine peanuts, flour, sugar, and salt in the bowl of a food processor. Pulse until peanuts are ground and mixture is well combined. Add butter and pulse again until mixture resembles coarse meal.
2Press mixture evenly into the prepared baking dish and prick it all over with a fork. Bake until lightly golden, about 30 minutes. Remove from the oven and place on a wire rack.
For the topping:
1Combine sugar, 1/2 teaspoon of the salt, and water in a medium saucepan. Bring to a boil over medium heat, stirring often until sugar is completely dissolved. Continue to boil mixture, swirling the pan occasionally (but not stirring), until it turns a deep caramel color, about 8 minutes. Remove the pan from heat and carefully stir in cream and vanilla extract (mixture will bubble up and steam).
2Sprinkle chopped chocolate evenly over cooled peanut shortbread.
3Stir peanuts into caramel mixture and immediately pour over shortbread and chocolate base. Sprinkle remaining 1/2 teaspoon salt over peanut bars and allow to finish cooling. Cut into rectangles and serve.