Preheat oven to 350. Grease a 9 inch springform pan.
In a food processor, crush the biscotti into crumbs. You should get a little over 1 1/2 cups. I went by weight and used 8 oz/half pound.
Add the sugar, melted butter and salt and pulse to mix. Empty into prepared cheesecake pan and press over bottom and just slightly up the sides.
Set crust on a rimmed baking sheet and bake for 10 minutes.
In a large mixing bowl, using an electric mixer, beat the cream cheese and sugar until smooth. add the egg yolks one at a time and beat on medium speed until blended. Still on medium speed or by hand if you prefer, fold in the sour cream and 1 teaspoon of the vanilla.
In another bowl, beat the egg whites until stiff peaks just start to form. Fold the beaten egg whites into the cheesecake batter.
Scrape the batter into the pan over the baked biscotti crust and bake for 30 minutes.
While the cheesecake is baking, stir together the remaining 8 oz of sour cream with the remaining 1/2 teaspoon of vanilla and the tablespoon of sugar.
After the cheesecake has baked for 30 minutes, remove from the oven and quickly spread the sour cream over the top. Return to the oven. Turn off the oven and let the cheesecake sit in the off oven for 2 hours.
Chill for several hours or overnight, then remove springform side and serve. Can be frozen.