Preheat the oven to 325°F (160°C).

In a mixing bowl, combine graham cracker crumbs, 1/2 cup granulated sugar, and melted butter. Press the mixture firmly into the bottom of the 9-inch springform pan.

Bake the crust for 10 minutes, then remove from the oven and let it cool.

In a large bowl, use an electric mixer to beat the softened cream cheese until smooth.

Add 1 cup granulated sugar and vanilla extract to the cream cheese, mixing until fully combined.

Add the eggs one at a time, mixing on low speed after each addition and scraping down the bowl sides.

Mix in the sour cream until the batter is smooth and lump-free.

Pour the cream cheese filling into the prepared crust and smooth the top with a spatula.

Bake for 60 minutes or until the center is just set and slightly wobbly.

Remove the cheesecake from the oven and allow it to cool in the pan to room temperature.

Refrigerate the cheesecake for at least 4 hours, preferably overnight, before removing from the pan and slicing.