Mix the graham cracker crumbs, butter, 1/4 cup of sugar, and flour together in a bowl; press into the bottom of a 9-inch springform pan.
Bake the crust until lightly browned, about 8 minutes; allow to cool in the pan. Raise the oven temperature to 450 degrees F (230 degrees C).
In a large bowl, beat the cream cheese with 1 3/4 cup of sugar, lemon peel, lemon juice, and vanilla extract until thoroughly combined. Beat in the eggs and egg yolks, one at a time, until the filling is free of lumps; gently fold in the whipped cream.
Bake in the 450-degree oven for 12 minutes, then reduce oven heat to 250 degrees F (120 degrees C). Bake until set, about 1 1/2 hours. Remove the cheesecake gently and carefully from the oven, and allow to cool to room temperature while still in pan; refrigerate overnight. Release the pan and gently remove to slice and serve the cheesecake.