Step 1: Prepare the Crust: In a medium bowl, combine the graham cracker crumbs, melted butter, and cup of sugar. Press the mixture firmly into the bottom of a 9-inch springform pan.
Step 2: Bake the Crust: Bake the crust in a preheated oven at 350F (175C) for 8-10 minutes, or until lightly golden. Remove from the oven and let it cool completely.
Step 3: Make the Cheesecake Filling: In a large bowl, beat the softened cream cheese with an electric mixer until smooth and creamy. Gradually add the 1 cups of sugar and salt, beating until well combined.
Step 4: Add Eggs and Egg Yolks: Beat in the eggs and egg yolks one at a time, mixing well after each addition. Be careful not to overmix, as this can cause the cheesecake to crack.
Step 5: Incorporate the Sour Cream and Vanilla: Stir in the sour cream and vanilla extract until just combined. The batter should be smooth and creamy.
Step 6: Pour Filling into Crust: Pour the cheesecake filling over the cooled crust, spreading it evenly.
Step 7: Bake the Cheesecake: Bake in the preheated oven for 55-65 minutes, or until the edges are set but the center still has a slight jiggle. If the top starts to brown too quickly, tent it with foil.
Step 8: Cool and Chill: Turn off the oven and let the cheesecake cool inside the oven with the door slightly ajar for 1 hour. This helps prevent cracking. Remove from the oven and let it cool completely at room temperature, then cover and chill in the refrigerator for at least 4 hours, or preferably overnight.
Step 9: Serve: Before serving, run a thin knife around the edge of the pan to loosen the cheesecake. Remove the sides of the springform pan and slice the cheesecake into wedges. Serve chilled.
Optional: For a richer flavor, use full-fat cream cheese and sour cream. A water bath can be used during baking to further prevent cracking. Simply wrap the bottom of the springform pan in foil and place it in a larger pan filled with about an inch of hot water.