Preheat your oven to 350°F (175°C).

In a mixing bowl, cream together the softened butter and powdered sugar until light and fluffy.

Gradually mix in the all-purpose flour and vanilla extract until a dough forms.

Press this dough into the bottom of a greased 9x9-inch baking pan. Bake for about 15-18 minutes, or until lightly golden. Set aside to cool.

In a large bowl, beat the softened cream cheese and granulated sugar until smooth.

Add the eggs, one at a time, mixing well after each addition.

Toss in the ground cinnamon and mix again to combine.

In a separate bowl, mix the sliced apples with lemon juice to prevent browning.

Fold the apples into the cheesecake mixture carefully, ensuring they are evenly distributed.

Pour the cheesecake and apple mixture over the cooled shortbread crust in the baking pan. Spread it out evenly.

Bake at 350°F (175°C) for 30-35 minutes, or until the cheesecake is set but still slightly jiggly in the center.

Let the bars cool at room temperature, then refrigerate for at least 3 hours before slicing them into squares for serving.