Preheat oven to 375 degrees Fahrenheit. Wrap the springform pan in an 18-inch piece of heavy-duty foil, working carefully to make sure there are no cracks or openings in the first 2-inches of the foil sides.
Pulse graham crackers in a food processor until they are fine crumbs. If you do not have a food processor then you can crush the crackers in a zip-top bag with a rolling pin.
Transfer the graham cracker crumbs to a medium bowl and stir in the sugar and melted butter, mixing well until fully combined.
Using a flat-bottomed measuring cup or glass, press the crumb mixture into the bottom and sides of a springform pan.
Bake for 8 minutes. Remove from the oven and reduce the temperature to 325°F.
Before the crust has cooled, check to see if the sides have fallen or cracked. While it is still warm you can use a cup to press the crust back into place.
Beat the cream cheese on medium-high speed for 1 minute. Add sugar and resume on medium-high speed for 3 minutes. Scrape the sides and bottom of the bowl.
Add flour and mix gently. Add vanilla and lemon juice and mix in at low speed until combined.
Add the eggs and egg yolks, one at a time, beating on low speed in between each addition. Scrape the bowl before adding the next egg.
Mix sour cream into the mixture, using low speed. It should be fully mixed into the batter but you do not want to beat it at this point or overmix.
Pour the cheesecake batter over the graham cracker crust and use a spoon or spatula to smooth the batter.
In a small bowl, mix together the oats, flour, brown sugar, cinnamon, and salt.
Add the melted butter and stir until the mixture becomes crumbly.
Layer the diced apples on top of the cheesecake batter, then top with the crumb mixture.
Recommended water bath: Place the cheesecake pan into a large roasting pan. Carefully fill the pan 1-inch full with boiling water, being careful to not splash any water onto the cheesecake.
Bake the cheesecake at 325°F and continue cooking for 90-100 minutes, or until the cheesecake has set.
Turn the oven off and crack open the oven door, allowing the cheesecake to cool for 1 hour without moving it from the oven.
Remove from the oven. Run a knife around the edge of the pan so that the cheesecake does not stick. Place plastic wrap over the top of the cheesecake and place in the refrigerator for at least 8 hours, or overnight.
Pour granulated sugar and water into a medium saucepan. Heat on medium-high heat until the sugar melts and turns an amber color.
Add heavy cream and cook while whisking continually for 3-4 minutes. Remove from heat.
Stir in butter and salt. Set aside to cool. When ready to serve drizzle the caramel sauce over the cheesecake.
If you have an instant-read thermometer, you can insert it in the center of the cheesecake to check doneness. The cheesecake is done once the center reaches 150°F.Substitutions:If using digestive biscuits instead of graham crackers, reduce the sugar in the crust to ¼ cup.You can substitute Greek yogurt for the sour cream in a 1:1 exchange.