Preheat oven to 350°F (175°C). Line a 9x13-inch baking pan with parchment paper. In a bowl, combine graham cracker crumbs, melted butter, and sugar. Mix until the texture resembles wet sand. Press firmly into the pan to form an even crust. Bake for 8–10 minutes, then let cool slightly.
In a large bowl, beat softened cream cheese and sugar until smooth and fluffy. Add eggs one at a time, mixing well after each addition. Stir in vanilla. Spread this cheesecake mixture evenly over the cooled crust.
Toss diced apples with cinnamon, nutmeg, and sugar. Sprinkle evenly over the cheesecake layer.
In a bowl, mix flour, brown sugar, and oats. Cut in cold butter using a pastry cutter or fork until crumbly. Sprinkle over the apples.
Bake in preheated oven for 40–45 minutes, or until the topping is golden and the cheesecake is set. The center may jiggle slightly but will firm up as it cools.
Allow the bars to cool completely at room temperature. Refrigerate for at least 3 hours, or overnight, before slicing.
Slice into squares and drizzle with caramel sauce just before serving.
