Preheat oven to 300F
Line a springform pan with a pie crust, pressing it around the sides of the pan and set aside.
Add the cream cheese, sour cream, vanilla extract and sugar to a medium bowl. Beat until creamy
Pour the cream cheese mixture into the pie crust lined springform pan and bake for 1 hour and 15 mintues.
While the cheesecake is baking, prepare the apples and other pie crust.
Peel and thinly slice the apples, then toss in the lemon juice.
In a medium microwave safe bowl, mix the flour, ground cinnamon, and sugar. Pour the flour-sugar mixture over the apple slices and toss.
Scatter the 6 tablespoons of butter on the top of the apple mixture. Place in the microwave for 45 second increments. Stir after each increment. It will take about 3 minutes total to melt butter and soften the apple slices. This process will basically cook the apple slices as well as produce an apple sugary juice.
After baking, turn off the oven and let the cheesecake cool inside for 1 hour. Do not open the oven door during this time.
Remove from the oven and top the cheesecake with the apple mixture.
Brush on an egg wash mixture onto the pie crust pieces: beat the 1 egg with 1 tbsp of water.
Starting on one side of the cheesecake, place one pie crust triangle. Work your way all the way around the cheesecake, making sure to overlap the previous triangle.
Increase the oven temperature to 425F.
Place the cheesecake back into the oven and cook for another 25 minutes, or until the pie crust is a golden brown.
Remove the cheesecake from the oven and allow to cool on the counter for at least 1 hour.
Living the cheesecake in the springform pan, wrap with it up with plastic wrap and place in the refridgerator for 2 hours to finish chilling.