Preheat oven to 350°F. Line a 9x13 inch baking pan with parchment paper, leaving about 2 inches of overhang on two opposite sides for easy lifting. Mix graham cracker crumbs, melted butter, sugar, and cinnamon until mixture resembles wet sand. Press firmly into pan bottom and bake for 10 minutes until edges begin to turn golden. Let cool.

Beat softened cream cheese with sugar using electric mixer for 2-3 minutes until smooth and fluffy. Add eggs one at a time, beating well after each addition. Stir in vanilla extract. Pour mixture over cooled crust and spread evenly to edges.

Toss diced apples immediately with lemon juice, then add brown sugar, cinnamon, and nutmeg. Distribute apple mixture evenly over cheesecake layer.

Combine flour and brown sugar in bowl. Cut in cold butter cubes using pastry cutter or fork until mixture forms pea-sized crumbles. Stir in pecans if using. Sprinkle streusel topping evenly over apples.

Bake for 45-50 minutes until streusel turns deep golden brown and cheesecake layer is set when pan is gently shaken. The cheesecake should still have a slight jiggle in the center - it will continue setting as it cools. Cool completely at room temperature for about 1 hour, then refrigerate for at least 2 hours before cutting.

For caramel sauce, combine sugar and water in saucepan over medium heat, stirring until sugar dissolves. Increase heat and cook without stirring until mixture turns rich amber color, watching carefully. Remove from heat, wait 10 seconds for bubbling to subside, then slowly whisk in cream while stirring constantly (will bubble vigorously). Add butter and salt, stirring until glossy and smooth. Makes approximately 1 cup. Drizzle warm caramel over bars before serving.