Combine the flour, sugar, and a pinch each of salt and cayenne pepper in a large bowl. Cut in the cream cheese and butter with a pastry blender or two knives until the mixture resembles coarse crumbs.
Combine the sour cream and 1 tablespoon iced water in a small bowl. Stir into the flour mixture until just combined. Flatten into a round, wrap in plastic wrap, and refrigerate for 1 hour or overnight.
Preheat the oven to 180°C. Roll the dough out to a 33 cm round on a lightly floured surface. Fit into a 23 cm pie plate with a removable bottom. Prick the bottom of the shell with a fork in several places. Line with foil and weight down with pie weights or dried beans.
Bake for 20 minutes or until the crust is beginning to set. Remove the pie weights and foil and bake for a further 15 minutes or until the crust is cooked through. Leave the oven on.
Whisk together the milk, whole eggs, egg whites, mustard and chives in a medium bowl. Stir in the Gruyère. Place the pie plate on a baking tray with sides. Pour the cheese mixture into the crust and bake for 35 minutes or until puffed and golden brown. Serve the tart warm or at room temperature.