Caramel popcorn: Coat 2 rimmed baking sheets with nonstick cooking spray. Heat oil in a large pot over medium-high heat until hot but not smoking. Add popcorn and cover. Cook, shaking pot frequently, until corn has finished popping. Transfer to a large bowl; stir in peanuts.
Heat butter, brown sugar, corn syrup, and salt in a medium saucepan over medium-high heat, stirring, until sugar is dissolved and butter is melted, 5 minutes. Continue to cook until mixture reaches 290 degrees on a candy thermometer, then remove from heat and quickly stir in vanilla and baking soda, making sure soda is dissolved fully. Drizzle half of caramel over popcorn mixture; pour remainder onto one baking sheet and let cool. Quickly toss popcorn to coat, then transfer to other baking sheet; let cool completely. Break caramel popcorn into bits. Popcorn can be stored in a resealable plastic bag at room temperature up to 5 days.
Caramel-chunk ice cream: Finely chop sheet of cooled caramel. Working in 2 batches, soften ice cream with an electric mixer on medium speed. Beat half of chopped caramel into each batch until thoroughly combined. Freeze until firm, 2 hours.
Hot-fudge sauce: Heat brown sugar and cocoa in a heatproof bowl set over a pan of simmering water, whisking to combine. Add cream and corn syrup and whisk until smooth. Cook, whisking occasionally, until mixture thickens slightly, about 10 minutes. Stir in chocolate, butter, vanilla, and salt and cook, stirring occasionally, until chocolate and butter are melted and sauce is smooth, 2 to 3 minutes. Let cool slightly. Sauce can be stored in refrigerator up to 5 days; reheat over low heat before serving.
To serve, layer ice cream in glasses with warm hot fudge and caramel popcorn.