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Preheat the oven to 300F and generously grease a 9-inch springform pan. Cut a circle of parchment to fit the bottom the pan and grease the paper. Wrap 2 pieces of aluminum foil around the outside of the pan to cover the bottom and most of the way up the sides.
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In a large bowl, beat the cream cheese and butter for 1 to 2 minutes, until completely smooth. Then beat in the sweetener until well combined.
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Add the sour cream, lemon zest, and vanilla extract and beat until smooth. Scrape down the beaters and the sides of the bowl as needed.
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Add the eggs, once at a time, beating each until just barely combined. Pour into the prepared springform pan and smooth the top.
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Set the pan inside a roasting pan large enough to prevent the sides from touching. Place the roasting pan in the oven and carefully pour boiling water into the roasting pan until it reaches halfway up the sides of the springform pan.