Preheat your oven to 350 degrees Fahrenheit. Line a 9x13-inch baking pan with parchment paper, leaving overhang on two sides for easy removal.

In a medium bowl, combine graham cracker crumbs, melted butter, sugar, and cinnamon. Stir until the crumbs are evenly moistened.

Press the crumb mixture firmly into an even layer on the bottom of the prepared pan. Bake for 10 minutes, then remove from the oven and let cool slightly.

In a large bowl, beat the softened cream cheese and sugar with an electric mixer on medium speed until smooth and creamy, about 2 minutes.

Add the eggs one at a time, beating well after each addition until just combined. Stir in the vanilla extract.

Pour the cheesecake batter over the warm crust and spread it evenly with a spatula.

In a separate bowl, toss the diced apples with lemon juice, brown sugar, cinnamon, and nutmeg until well coated.

Evenly distribute the apple mixture over the cheesecake layer, pressing down lightly.

In a small bowl, whisk together the flour and brown sugar. Add the cold butter cubes and use a pastry cutter or your fingertips to cut the butter into the dry mixture until it resembles coarse crumbs.

Stir in the chopped pecans if using. Sprinkle the streusel evenly over the apple layer.

Bake for 45 to 50 minutes, until the streusel is golden brown and the cheesecake is set around the edges but still slightly jiggly in the center.

Let the bars cool completely on a wire rack at room temperature, then cover and refrigerate for at least 2 hours (or up to overnight) to fully set.

In a medium heavy-bottomed saucepan, combine the sugar and water. Heat over medium heat, stirring gently, until the sugar dissolves and the mixture is clear.

Increase the heat to medium-high and bring to a boil. Cook without stirring until the syrup turns a deep amber color, about 8 to 10 minutes. Watch closely to prevent burning.

Remove from heat and carefully pour in the heavy cream while whisking constantly (the mixture will bubble up vigorously). Whisk until smooth.

Add the butter and salt, stirring until the butter is fully melted and the sauce is silky. Let cool slightly before drizzling.

Using the parchment overhang, lift the chilled block of bars onto a cutting board. Cut into 16 squares with a sharp knife, wiping the blade clean between cuts.

Drizzle each bar with warm caramel sauce just before serving. Extra sauce can be stored in the refrigerator for up to 2 weeks.