Preheat the oven to 300°F.
Line a large baking sheet with parchment paper and set it aside.
Place the popped popcorn in a large mixing bowl.
Core the apples and cut them into small, evenly sized pieces, about ½ inch each.
Pat the chopped apples gently with a clean kitchen towel or paper towel to remove excess surface moisture.
Add the apples to the popcorn and gently toss them together.
Measure the heavy cream and warm it slightly. It should be warm but not boiling.
Stir the vanilla extract and kosher salt into the warm cream and set aside.
Add the sugar to a small heavy-bottomed saucepan and place it over medium heat.
Allow the sugar to begin melting. Gently swirl the pan occasionally as it melts, but avoid vigorously stirring while dry sugar remains.
Continue cooking until all of the sugar has melted and the caramel reaches a deep amber color. If using a candy thermometer, the caramel should reach about 350°F.
Remove the saucepan from the heat.
Slowly pour the warm cream mixture into the caramel while whisking continuously. The mixture will bubble vigorously, so pour carefully.
If the caramel clumps or seizes, return the saucepan to low heat and continue stirring until it becomes smooth again.
Once the caramel is smooth and completely combined, remove it from the heat.
Carefully pour the hot caramel over the popcorn and apples.
Using a rubber spatula or wooden spoon, gently fold everything together until the popcorn and apple pieces are evenly coated.
Spread the caramel-coated popcorn and apples evenly over the prepared baking sheet.
Bake for 10 minutes.
Carefully remove the pan from the oven and gently stir the popcorn.
Return the pan to the oven and bake for another 10 to 15 minutes, or until the caramel has thickened and is clinging well to the popcorn and apples.
Remove the pan from the oven and give the popcorn one final gentle stir.
Allow the caramel apple popcorn to cool completely for about 1 hour.
Once the popcorn has cooled, melt the dark chocolate chips in a double boiler or in a heat-safe bowl set over a saucepan of gently simmering water.
Stir until the chocolate is smooth.
Dip the tines of a fork into the melted chocolate and drizzle it over the caramel apple popcorn.
Allow the chocolate to set before serving.