Bring butter, sugar, and salt to a boil in a 4- to 5-quart heavy pot over medium-high heat, whisking until smooth, then boil, stirring occasionally, until mixture is deep golden and registers 300°F (hard-crack stage; see Kitchen Notebook, page 240) on thermometer, 15 to 20 minutes.
Immediately stir in whole peanuts, then carefully pour hot toffee into center of baking pan. Spread with spatula, smoothing top, and let stand 1 minute, then immediately sprinkle chocolate on top. Let stand until chocolate is melted, 4 to 5 minutes, then spread over toffee with cleaned spatula. Sprinkle evenly with chopped peanuts, then freeze until chocolate is firm, about 30 minutes. Break into pieces.