Preheat your oven to 350°F (175°C). Line a 9×13 inch baking pan with parchment paper, letting it hang over the edges by about 2 inches on each side for easy removal.
Mix graham cracker crumbs, melted butter, 1/4 cup granulated sugar, and 1/4 teaspoon cinnamon in a bowl until it resembles wet sand. Press firmly into the bottom of the prepared pan to about 1/4-inch thickness.
Bake the crust for 10 minutes. Remove from oven and let cool for at least 5 minutes.
Beat softened cream cheese and 1/2 cup granulated sugar with an electric mixer on medium speed for 2-3 minutes until smooth and fluffy. Add eggs one at a time, mixing on low speed after each just until combined. Stir in vanilla extract.
Pour cheesecake mixture over the cooled crust and spread evenly.
Toss diced apples with lemon juice, 1/4 cup brown sugar, 1 teaspoon cinnamon, and nutmeg. Spread evenly over cheesecake layer.
Mix flour and 1/4 cup brown sugar in a clean bowl. Cut in cold butter cubes until pea-sized crumbles form. Stir in chopped pecans if using.
Sprinkle streusel topping evenly over the apple layer.
Bake for 45-50 minutes, until streusel is golden brown and cheesecake is set with slight jiggle in center. Cool at room temperature 1-2 hours.
Refrigerate bars at least 2 hours or overnight before cutting.
For caramel sauce, combine 1 cup sugar and water in saucepan over medium heat, stirring until sugar dissolves.
Increase heat to medium-high and cook without stirring, swirling pan occasionally until deep amber color, about 8-10 minutes.
Remove from heat, whisk in warm heavy cream carefully, then stir in butter and salt until smooth. Cool 5-10 minutes.
Lift bars from pan using parchment overhang. Cut into 24 squares, wiping knife between cuts.
Let bars sit at room temperature 15 minutes, drizzle with warm caramel sauce just before serving.