In a small bowl, stir the sour cream together with the vanilla. In another small bowl, add 1 tablespoon of the sour cream mixture from the other bowl. Stir in the flour until very smooth, them add more of the sour cream mixture until you have added it all. Set aside.
In the bowl of a stand mixer or in a large bowl with a hand mixer, whip, using the whisk attachment, the egg yolks until lemon colored and thick. Beat in 1 cups of sugar until very smooth, reserving the 1/4 cup plus 1 tablespoon remaining for whipping the egg whites.
Change to the paddle attachment on your mixer. Break the cream cheese in small pieces and add to the mixing bowl, adding small amounts at a time. Mix on medium, for several minutes. Then increase the speed to medium high and continue mixing until completely combined and smooth. There should be next to no lumps! Beat in the sour cream/flour mixture. Beat until smooth on medium speed.
Scrap the batter into another large bowl.
Clean the stand mixer bowl and whisk attachment and dry completely, as any water drops in your bowl will keep the whites from whipping properly. Using the whisk attachment, whisk the egg whites on medium speed until fine bubbles form. Shake in slowly the 1/4 cup, plus 1 tablespoon of remaining sugar in with the mixer on medium high speed. Increase the speed to high and continue whipping until stiff and glossy, but not dry.
Fold the whipped egg whites gently in the cream cheese mixture, mixing in a third of the whipped whites at a time. Pour the batter over the over the crust, smoothing the top.
Bake at 285 for 90 minutes, then without opening the oven door, turn oven off and leave the cheesecake in the oven for 1 hour. You can look at the cheesecake through the oven door with the light, but don't open during baking or the hour following.
Remove to a wire rack to finish cooling, before covering with cellophane and foil or parchment and foil over.
Place covered cheesecake in the refrigerator. Refrigerate overnight, as the cheesecake should be served chilled.
Serve plain or with Chocolate Brandy Sauce or any toppings you desire. Makes 10 - 12 servings.