Combine the vegetable oil and 1 popcorn kernel in a heavy pot over high heat; cover. When it pops, add the rest of the kernels. Partially cover and cook, shaking the pot, until you no longer hear the popping sounds. Remove from the heat and spread the popcorn on a baking sheet.
In the same pot, melt the butter over medium heat. Add the toffee chips and peanuts and stir until the toffee melts and evenly coats the peanuts, about 2 minutes, adding more butter if needed. Pour the mixture over the popcorn. Use a rubber spatula to toss the popcorn and toffee sauce to evenly coat.
Put the chocolate chips in a small microwave-safe bowl and microwave in 30-second intervals, stirring, until melted. Dip a whisk in the melted chocolate and use it to drizzle over the popcorn. Let harden before serving.