In a large mixing bowl, use an electric hand mixer or a stand mixer fitted with the whisk attachment to beat the cream cheese until smooth.
Add the granulated sugar. Mix until fully incorporated, scraping down the sides of the bowl as needed.
Mix in the sour cream and vanilla extract until smooth.
With the mixer on low speed, add the eggs one at a time, mixing until just combined after each addition. Do not overmix.
Pour the batter into the prepared crust, smoothing the top with a spatula.
Place the springform pan into a larger roasting pan. Then, carefully pour hot water into the roasting pan until it reaches about halfway up the sides of the springform pan.
Bake for 60 to 70 minutes, or until the top is lightly golden and the center is just set but slightly jiggly.
Turn off the oven. Let the cheesecake cool in the oven with the door slightly ajar for 1 hour.
Transfer to a wire rack and let cool completely.