Position the oven racks in the center of the oven and preheat to 350°F (175°C).

In a medium mixing bowl, combine the crushed graham crackers, melted butter, and granulated sugar. Mix until evenly moistened. Press the mixture firmly into the bottom and halfway up the sides of a springform pan using the bottom of a flat glass or measuring cup.

Bake the crust for 7 minutes. Remove from the oven and set aside to cool. Reduce the oven temperature to 325°F (165°C).

In a large mixing bowl, beat the cream cheese until completely smooth and free of lumps. Add the granulated sugar, sour cream, and vanilla extract. Mix thoroughly, scraping down the sides of the bowl as needed to ensure a uniform texture.

In a separate bowl, lightly beat the eggs with a fork. Gradually add the eggs to the cream cheese mixture on low speed, mixing only until incorporated. Do not overmix.

Gently tap the mixing bowl on the countertop several times to release any trapped air bubbles.

Pour the cheesecake filling into the prepared crust and smooth the surface evenly. The pan will be nearly full.

Bake at 325°F (165°C) for 30 minutes. Reduce the oven temperature to 250°F (120°C) and continue baking for an additional 45 minutes. The center should remain slightly jiggly.

Turn off the oven and leave the cheesecake inside with the door closed for 30 minutes. Then crack the oven door open and allow the cheesecake to cool inside for 1 hour.

Remove the cheesecake from the oven and allow it to cool at room temperature for 3 to 4 hours. Cover and refrigerate for at least 6 hours, or overnight, until fully set.

Garnish with desired toppings before serving.