Step 1: Preheat your oven to 350°F (175°C). Lightly grease a 9-inch springform pan.
Step 2: In a medium bowl, combine the graham cracker crumbs, 1/4 cup granulated sugar, and melted unsalted butter. Mix until well combined and the crumbs are evenly moistened.
Step 3: Press the crumb mixture firmly and evenly into the bottom of the prepared springform pan. You can use the bottom of a glass or a flat measuring cup to help compact the crust.
Step 4: Bake the crust for 8-10 minutes, or until lightly golden. Remove from the oven and let cool completely on a wire rack while you prepare the filling.
Step 5: Reduce oven temperature to 325°F (160°C).
Step 6: In a large mixing bowl, using an electric mixer on medium speed, beat the softened cream cheese until completely smooth and creamy, about 2-3 minutes. Scrape down the sides of the bowl frequently.
Step 7: Gradually add the 1 3/4 cups granulated sugar to the cream cheese, beating until just combined and smooth. Do not overbeat.
Step 8: Beat in the sour cream, lemon juice, and vanilla extract until just incorporated.
Step 9: Add the eggs one at a time, beating on low speed only until each egg is just blended into the batter. This is a critical step to prevent cracks. Overmixing introduces too much air.
Step 10: Pour the cheesecake batter 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 11: Wrap the bottom of the springform pan tightly with heavy-duty aluminum foil to prevent any potential leaks.
Step 12: Bake the cheesecake for 60-75 minutes, or until the edges are set but the center (about a 2-3 inch circle) still jiggles slightly when the pan is gently nudged. The internal temperature should be around 150°F (65°C).
Step 13: Turn off the oven, but leave the cheesecake inside with the oven door ajar (prop it open with a wooden spoon) for 1 hour. This slow cooling prevents drastic temperature changes.
Step 14: Remove the cheesecake from the oven and carefully remove the foil. Let it cool completely on a wire rack at room temperature for another 1-2 hours.
Step 15: Once completely cool, cover the cheesecake with plastic wrap and refrigerate for at least 6 hours, or preferably overnight. Chilling is essential for firming up and flavor melding.
Step 16: To serve, run a thin knife around the edge of the pan before releasing the springform sides. Slice with a hot, clean knife for perfect slices. Enjoy!