Start by preparing your apples. Wash and dry them thoroughly, then slice them into even wedges. Remove the seeds and core as needed.
In a medium saucepan over medium heat, combine the granulated sugar, brown sugar, and butter. Stir until the mixture melts and begins to bubble, about 3 to 5 minutes.
Gradually add the heavy cream to the saucepan. Be careful as it may bubble up. Stir continuously for about 3 to 4 minutes until the mixture thickens slightly.
Remove the saucepan from the heat and stir in the vanilla extract and salt until well incorporated.
Let the caramel cool slightly for about 5 minutes to thicken a bit more. This will help it adhere better to the apple slices.
While the caramel cools, prepare a baking sheet lined with parchment paper for the dipped apple slices.
Dip each apple slice into the warm caramel, allowing any excess to drip off before placing it on the prepared parchment. Repeat with all apple slices.
If desired, sprinkle chopped nuts or drizzle melted chocolate over the caramel-coated slices for added flavor and texture.
Allow the caramel to set at room temperature for about 10 to 15 minutes before serving.