Prepare the crust

Preheat your oven to 350°F (175°C). Line an 8×8 baking pan with parchment paper. Mix the graham crumbs, melted butter, and sugar until everything feels like damp sand. Press firmly into the bottom of the pan to form an even crust. Bake for 8–10 minutes, then set aside to cool slightly.

Make the apple filling

In a small pan, melt the butter over medium heat. Add the diced apples, brown sugar, cinnamon, and lemon juice. Cook for about 5 minutes, stirring gently, until the apples soften but still hold their shape. Remove from heat and let them cool.

Mix the cheesecake layer

In a large bowl, beat the softened cream cheese until smooth and fluffy. Add the sugar and mix again. Then add the eggs one at a time, followed by the vanilla. Mix just until combined—overmixing can cause cracking.

Assemble the bars

Pour the cheesecake mixture over the baked crust and smooth the top. Spoon the cooled apples evenly across the cheesecake layer.

Prepare the crumb topping

In a small bowl, combine the flour, brown sugar, cinnamon, and cold butter. Use your fingertips to rub the butter into the mixture until it forms soft crumbs. Sprinkle evenly over the apples.

Bake

Bake the assembled bars for 30–35 minutes, or until the center is just set. The edges will be slightly golden, and the topping lightly crisp.

Chill and serve

Let the bars cool completely, then refrigerate for at least 2 hours. Before serving, slice into squares and finish with a generous drizzle of caramel.