Step 1

Preheat the oven to 325° and position a rack in the center. Butter a 9-inch-square nonstick baking pan. In a food processor, pulse the flour with the sugar, lemon zest and salt. Add the butter and pulse until a soft, crumbly dough forms. Press the dough evenly over the bottom and a scant 1/2 inch up the side of the pan. Bake the crust for 20 minutes, or until golden and firm.

Step 2

In a small bowl, dissolve the cornstarch in the water. In a medium sauce-pan, whisk the egg yolks with 3/4 cup of the sugar and the lemon juice. Whisk in the cornstarch mixture and cook over moderate heat, whisking gently, until the sugar is dissolved and the lemon mixture is hot, about 4 minutes. Boil over moderately high heat for 1 minute, whisking constantly, until the mixture is thick and glossy. Strain the lemon mixture into a heatproof bowl. Stir in the lemon zest and let cool.

Step 3

In a large bowl, using an electric mixer, beat the cream cheese with the remaining 1 cup of sugar until smooth. Beat in the flour until blended. Add the eggs, 1 at a time, beating well between additions. Add the sour cream and the vanilla and beat until the batter is smooth. Pour the cream cheese batter over the crust and smooth the surface with a spatula. Dollop the lemon mixture on the cheesecake batter and carefully swirl it into the batter; take care not to cut into the crust.

Step 4

Bake the cheesecake for about 40 minutes, or until golden around the edge and just set. Run the tip of a knife around the edge to loosen the cheesecake from the side of the pan. Let cool on a wire rack for 1 hour, then refrigerate the cheesecake until thoroughly chilled. Cut into 16 bars and serve.