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Preheat the oven to 325°. Butter the sides only of a 9-inch springform pan. In a bowl, stir the graham cracker crumbs with the sugar and butter until moistened. Press the crumbs into the bottom of the springform pan in an even layer.
In a large bowl, using an electric mixer, beat the cream cheese with 1/2 cup of the sugar until smooth. Add the egg yolks, lemon zest and olive oil and beat until smooth.
In another bowl, beat the egg whites at medium speed until frothy. Increase the speed to high and beat until firm peaks form. Slowly add the remaining 3 tablespoons of sugar and beat until the whites are stiff and glossy. Beat one-fourth of the whites into the cream cheese mixture, then fold in the rest until no streaks remain. Scrape the filling into the pan and smooth the surface.
Bake the cheesecake in the center of the oven for 45 minutes, or until the top is golden and lightly cracked. Transfer the cheesecake to a rack to cool completely, then refrigerate until chilled, at least 2 hours.
Remove the ring and transfer the cheesecake to a plate. Cut into wedges and serve.
The cheesecake can be refrigerated for up to 3 days.