Step 1: Preheat your oven to 350°F (175°C). Wrap the outside of a 9-inch springform pan tightly with several layers of heavy-duty aluminum foil to prevent water from seeping in during the water bath. Ensure the foil goes up the sides.
Step 2: Prepare the crust: In a medium bowl, combine graham cracker crumbs, ¼ cup sugar, and melted butter. Mix until fully moistened. Press the mixture firmly and evenly into the bottom of the prepared springform pan using the back of a spoon or a flat-bottomed glass. Bake for 10 minutes. Remove from oven and let cool completely on a wire rack while you prepare the filling.
Step 3: Reduce oven temperature to 325°F (160°C).
Step 4: Prepare the filling: In a large mixing bowl, using an electric mixer on medium speed, beat the softened cream cheese until completely smooth and free of any lumps, about 2-3 minutes. Scrape down the sides of the bowl frequently to ensure even beating.
Step 5: Gradually add 1 ½ cups sugar, beating on low speed until just combined and smooth. Scrape down the bowl again to ensure no sugar remains unmixed.
Step 6: Beat in the all-purpose flour, vanilla extract, and salt until just incorporated. Continue to scrape down the bowl.
Step 7: Add the eggs one at a time, beating on low speed *just until the yolk disappears* after each addition. This step is critical: do not overmix! Overmixing incorporates too much air, which can cause cracks in your finished cheesecake.
Step 8: Gently fold in the sour cream or heavy cream with a spatula until smooth. Ensure there are no streaks of unmixed cream cheese or sour cream, but again, avoid overmixing.
Step 9: Pour the smooth cheesecake filling over the cooled crust in the springform pan. Gently tap the pan on the counter a few times to release any large air bubbles.
Step 10: Prepare the water bath: Place the foil-wrapped springform pan into a larger roasting pan. Carefully pour hot (but not boiling) water into the roasting pan, ensuring it reaches about halfway up the sides of the springform pan. Be careful not to splash water into the cheesecake batter.
Step 11: Carefully transfer the roasting pan with the cheesecake to the preheated oven. Place it on the middle rack.
Step 12: Bake for 1 hour to 1 hour 15 minutes, or until the edges are set and slightly puffed, but a 2-3 inch circle in the center still has a slight jiggle when gently shaken. Do not overbake! The center will continue to set as it cools.
Step 13: Turn off the oven, prop the door open slightly with a wooden spoon or oven mitt, and let the cheesecake cool in the oven for 1 hour. This gradual cooling prevents sudden temperature changes that can shock the cheesecake and lead to cracks.
Step 14: Remove the cheesecake from the water bath and the roasting pan. Carefully remove the foil from around the springform pan. Let it cool completely on a wire rack at room temperature for another 1-2 hours.
Step 15: Once completely cool, cover the cheesecake loosely with plastic wrap and refrigerate for at least 6-8 hours, or preferably overnight, until thoroughly chilled and set. This chilling time is crucial for the cheesecake's texture and stability.
Step 16: Before serving, run a thin knife around the edge of the pan to loosen the cheesecake, then release the springform collar. For the cleanest slices, use a long, thin knife warmed under hot water and wiped dry between each cut. Serve plain or with your favorite toppings.