Prepare the Crust: Preheat your oven to 325°F (163°C). In a mixing bowl, combine graham cracker crumbs, sugar, and melted butter. Mix until the crumbs are evenly coated and the texture resembles wet sand. Press the mixture firmly into the bottom of a 9-inch (23 cm) springform pan to form an even layer. Bake the crust for 10 minutes, then set aside to cool while preparing the filling.

Make the Cheesecake Filling: In a large mixing bowl, beat the softened cream cheese and granulated sugar together using an electric mixer on medium speed until smooth and creamy. Add the vanilla extract, then mix in the eggs one at a time, ensuring each egg is fully incorporated before adding the next. Blend in the egg yolks, followed by the heavy cream. Mix until just combined, avoiding overmixing to prevent air bubbles.

Assemble and Bake: Pour the cheesecake filling over the cooled crust, smoothing the top with a spatula. Place the springform pan in a larger baking dish, then fill the baking dish with about 1 inch of hot water to create a water bath. This helps prevent cracking. Bake the cheesecake at 325°F (163°C) for 75-90 minutes, or until the edges are set and the center jiggles slightly when gently shaken.

Cool and Chill: Turn off the oven, crack the door slightly, and let the cheesecake cool inside for 1 hour. Remove the cheesecake from the water bath and cool completely at room temperature. Cover and refrigerate for at least 4 hours, preferably overnight, to fully set before slicing and serving.