Preheat oven to 375F (190C).

Butter a 9-inch springform pan.

In a bowl, cream together butter, sugar, and vanilla extract until light and fluffy.

Gradually add flour and salt to the creamed mixture and blend until just combined.

Press the dough evenly into the bottom of the prepared springform pan.

In a separate bowl, beat cream cheese until smooth and fluffy.

Add sugar, egg, and vanilla extract to the cream cheese and beat until well combined.

Spread the cream cheese filling evenly over the crust in the pan.

In a small bowl, combine sugar and cinnamon.

Dip each apple slice in the cinnamon-sugar mixture, coating both sides.

Arrange the coated apple slices in two overlapping arches on top of the cream cheese filling.

Warm apricot preserves in a small saucepan or microwave until slightly thinned.

Brush the warmed apricot preserves evenly over the apple slices.

Bake in the preheated oven for 45-55 minutes, or until the cheesecake is golden brown and the filling is set.

Let the cheesecake cool slightly before removing the sides of the springform pan.

Serve warm or chilled.