Preheat your oven to 350°F (175°C). In a food processor, pulse together the graham cracker crumbs, granulated sugar for the crust, and melted unsalted butter until thoroughly combined. Press this mixture into the bottom and up the sides of a 9-inch springform pan.

In a large mixing bowl, beat the softened cream cheese on low speed until smooth, about 2 minutes. Gradually add in the granulated sugar for the filling while continuing to mix until creamy. Blend in the vanilla extract, then add the eggs one at a time, mixing until each is fully incorporated.

Pour the cheesecake filling over the prepared crust, smoothing the top with a spatula. Bake for 22-25 minutes, until the edges are set but the center jiggles slightly when shaken. Turn off the oven, crack the door open, and let the cheesecake cool for 45-60 minutes inside.

After cooling, allow it to reach room temperature for another 30 minutes. Cover loosely with plastic wrap and refrigerate for at least 4 hours, ideally overnight.

When ready to serve, run a knife around the edge of the pan before releasing the springform. Slice the cheesecake and serve as is or with favorite toppings.