Preheat the oven to 300F and generously grease a 9-inch round cake pan. Cut a circle of parchment to fit the bottom the pan and grease the paper.
FOR THE CRUST:
FOR THE FILLING:
In a large bowl, beat the cream cheese and butter until smooth, then beat in the sweetener until well combined. Add the eggs, once at a time, beating after each addition. Clean the beaters and scrape down the sides of the bowl as needed.
Add the sour cream, lemon zest, and vanilla extract and beat until the batter is smooth and well combined. Pour into the prepared springform pan and smooth the top.
BAKING:
Make a water bath. 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 pan.
Bake 70 to 90 minutes, until the cheesecake is mostly set but still jiggles just a little in the center when shaken.
Place a wooden spoon in the door of the oven to prop it open, and leave cheesecake inside for 1 hour or more.
Remove the roasting pan from the oven, then carefully remove the pan from the water bath. Continue to let cool to room temperature for one hour.
Cheesecake can be chilled for at least 3 hours or covered and stored overnight before serving.
REMOVING FROM PAN
Once the cheesecake has completely cooled, Unmold from the cake pan by placing the cooled cake back into the roasting pan filled again with warm water. Gently run a sharp knife around the edges of the cake to loosen.
You can serve the cake from the pan, or invert onto a glass plate covered in wax paper, then invert again onto a serving tray. Be sure your cake is very cold when you do this!