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Preheat oven to 350°F/180°C.
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In a medium bowl, stir crumbs and melted butter together until combined and moistened. Put mixture in a 9-inch springform pan and press with your fingers (or use the bottom of a glass) to form an even layer of crumbs. Bake for 8-10 minutes, until golden brown. Allow to cool completely on a wire rack. Meanwhile, prepare the filling.
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In a mixer fitted with the paddle attachment, beat cream cheese on medium-low speed until smooth and lump-free, about 1-2 minutes. Add sugar and beat until blended. Scrape down the sides and bottom of the bowl as necessary. Beat in eggs, one at a time, until fully combined. Add cream, vanilla extract, and lemon zest and beat just until combined and smooth. Pour batter over cooled crust and spread evenly.
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If baking in a water bath: After baking the crust, reduce oven temperature to 325°F/160°C. Wrap the bottom and sides of the pan with one large piece of foil, then repeat with another piece. This will ensure that water from the bath doesn’t seep into the cake. Place the pan inside a large roasting pan, then pour enough boiling water into the roasting pan to come halfway up the sides. Place gently in the oven and bake for 60-70 minutes or until the sides are set but the center is still slightly wobbly.
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If not baking in a water bath: After baking the crust, increase oven to 425°F/220°C. Bake cake for 10 minutes, then lower temperature to 225°F/110°C and continue baking for about an hour, or until the sides are set but the center is still slightly wobbly.
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Allow cake to sit at room temperature for 15 minutes, then prepare the topping by whisking together sour cream, powdered sugar, and vanilla extract until smooth, and pour it over the warm cake. Let cool completely to room temperature, then refrigerate for at least 4 hours, preferably more, until completely set.
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Cover cheesecake with plastic wrap and keep in the refrigerator for up to 5 days.