In a large bowl, combine 1 cup flour, 1/4 cup sugar and 2 teaspoons lime zest. Add vanilla and cut in butter until mixture resembles course crumbs. Add 1 egg yolk and stir until all flour is moistened. Gather dough into ball, wrap in wax paper and refrigerate for 1 hour and 30 minutes.
Lightly butter a 25cm springform cake tin. Roll dough on lightly floured surface to 3mm thick; trim to a circle a bit larger than the bottom of the tin. Reserve pastry trimmings. Press pastry circle into bottom and 1cm up sides of tin. Refrigerate 1 hour.
Preheat oven to 200 degrees C. Bake crust for 20 minutes, until lightly browned. Cool on wire rack.
Beat cream cheese, 1 3/4 cups sugar, 3 tablespoons flour and zest in large mixer on medium speed until light and fluffy, about 10 minutes. Add vanilla. Beat in 5 eggs and 2 egg yolks, 1 at a time, on medium speed. Stir in cream.
Increase oven temperature to 260 degrees C. Roll out reserved pastry trimmings on lightly floured board; cut into strips 5cm wide and use them to line the sides of the tin. Pour filling into crust. Bake 15 minutes.
Reduce oven temperature to 100 degrees C. DO NOT OPEN OVEN DOOR! Bake until cheesecake is firm in centre, about 50 minutes. Turn off oven; leave cheesecake in oven with door slightly open for 1 hour. Remove from oven and cool completely on wire rack. Refrigerate at least 2 hours.