Preheat the oven to 375 degrees F (190 degrees C).
Combine graham cracker crumbs, melted butter, and 2 tablespoons sugar in a bowl. Mix until evenly moistened; press into the bottom of a 9-inch springform pan and place in the refrigerator.
Beat cream cheese in a large bowl with an electric mixer until smooth and creamy. Add 1 cup sugar and beat until combined. Add eggs and 1 teaspoon vanilla extract; beat on high speed until creamy, about 1 minute. Pour cream cheese mixture into the chilled cracker crust and spread to evenly cover crust.
Pour enough water into a rimmed baking sheet to cover the bottom, and place the springform pan on top.
Bake in the preheated oven until golden brown, about 1 hour. Remove from the oven and increase oven temperature to 500 degrees F (260 degrees C).
Just before cheesecake finishes baking, combine sour cream, 2 tablespoons sugar, and 1/2 teaspoon vanilla extract in a bowl for the topping. Spread evenly on top of the cheesecake.
Return to the oven and bake for 5 minutes. Set the pan on a wire rack, and allow the cheesecake to cool at room temperature, about 1 hour. Refrigerate until completely chilled, about 4 hours, before serving.
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