Step 1: Prepare the Crust - In a medium bowl, combine the graham cracker crumbs, sugar, and salt. Pour in the melted butter and mix until the crumbs are evenly coated. Press the mixture firmly into the bottom of a 9-inch springform pan, creating an even layer. Bake at 350°F (175°C) for 10 minutes, then allow it to cool while you prepare the filling.
Step 2: Make the Filling - In a large mixing bowl, beat the cream cheese with an electric mixer on medium speed until smooth and creamy, about 2-3 minutes. Gradually add the granulated sugar and continue mixing until fully incorporated. Scrape down the sides of the bowl to ensure everything is well combined.
Step 3: Incorporate the Sour Cream and Vanilla - Add the sour cream and vanilla extract to the cream cheese mixture. Beat until smooth.
Step 4: Add the Eggs and Flour - Add the eggs and egg yolks one at a time, mixing well after each addition. Then, sift in the flour and mix until just combined. Be careful not to overmix.
Step 5: Incorporate the Heavy Cream - Slowly pour in the heavy cream and mix until the filling is silky and smooth.
Step 6: Prepare the Water Bath - Wrap the outside of the springform pan tightly with aluminum foil. Place the pan in a larger roasting pan and fill it with hot water until it reaches halfway up the sides of the springform pan.
Step 7: Bake the Cheesecake - Preheat your oven to 325°F (160°C). Pour the filling into the prepared crust and smooth the top with a spatula. Bake for 60-70 minutes, or until the edges are set but the center is still slightly jiggly. Turn off the oven and leave the cheesecake inside with the door ajar for 1 hour.
Step 8: Chill the Cheesecake - Remove the cheesecake from the water bath and let it cool at room temperature for another hour. Once cool, refrigerate for at least 4 hours, preferably overnight.