Preheat oven to 350°F and lightly grease a 9x13 baking dish. Wash and dry the apples, then slice about half an inch off the top of each one near the stem and set the tops aside.
Use an apple corer to remove the core from each apple, stopping about half an inch from the bottom. Use a melon baller or small spoon to widen the cavity, leaving sturdy walls about a half inch thick.
Brush the inside and cut edges of each apple with lemon juice to prevent browning. Arrange the hollowed apples upright in the prepared baking dish, nestling them close together.
In a mixing bowl, beat the softened cream cheese with an electric hand mixer until smooth and free of lumps, about 1 minute. Add the granulated sugar and beat again until fully combined.
Add the egg and vanilla extract, then mix on low speed just until incorporated. Avoid overmixing once the egg is added. Add the pinch of salt and stir with a spatula until evenly blended.
In a separate small bowl, combine the graham cracker crumbs, brown sugar, and ground cinnamon. Pour in the melted butter and stir with a fork until the mixture looks like wet sand and holds together when pressed. Fold in the chopped pecans if using.
Spoon the cheesecake filling into a piping bag or a zip-top bag with the corner snipped off. Pipe the filling into each hollowed apple, filling them almost to the top.
Sprinkle a generous spoonful of the crumb topping over the exposed filling on each apple, pressing down lightly so it adheres. Set the reserved apple tops loosely to the side of the dish.
Pour about 1/4 cup of water into the bottom of the baking dish. Loosely tent the dish with foil and bake for 20 minutes.
Remove the foil and continue baking for another 15 minutes, until the apples are fork tender and the crumb topping is golden brown. Keep an eye on the last few minutes.
Let the apples rest in the dish for at least 10 minutes before serving, since the cheesecake filling needs a little time to set. Drizzle each apple with caramel sauce right before serving.
Serve warm, either on their own or with a scoop of vanilla ice cream on the side.