Using an electric mixer or a stand mixer fitted with a paddle attachment, beat the cream cheese on medium speed until smooth and creamy.
Add the sugar. Continue to beat until the mixture is smooth and creamy, stopping to scrape down the sides of the bowl as needed.
Add the sour cream and vanilla. Blend until smooth and creamy, stopping to scrape down the sides of the bowl as needed.
With the mixer on low, add eggs, one at a time, until fully incorporated, scraping the bowl after each addition.
Add key lime juice and zest to the cream cheese mixture. Mix until just combined.
Pour the filling over the crust.
Carefully place the foil-lined springform pan into a larger pan and place both in the oven.
Pour hot water into the larger pan, about halfway up the side of the foil-lined pan. Using a teapot with hot water works very well, as it is easy to pour and the water is already hot.
Bake 70-80 minutes, or until the top of the cheesecake turns golden brown and the edges are set. The center may still be slightly jiggly. Remove from the oven and let cool on a wire rack.
Transfer to the refrigerator to chill for at least 4 hours, up to overnight.
Garnish with whipped cream, sliced limes, and extra zest from a key lime.