Preheat the oven to 350 degrees F. Grease the bottom and sides of a 9-inch springform pan with butter or shortening and wrap the outside bottom and sides tightly with two layers of foil (heavy-duty works best).
To make the crust, in a food processor add the graham crackers and brown sugar and crush into fine crumbs.
Gradually pour in the butter until the crumbs are coated. Firmly press the crumbs into the bottom of the springform pan, then bake it for 15 minutes.
Remove from oven and place the crust in a large roasting pan, set aside.
To make the cheesecake filling, lower the temperature of the oven to 325 degrees F. In a large bowl, blend the cream cheese, sugar, flour, vanilla extract, yogurt, and vanilla beans until the cream cheese is smooth and lump-free.
Mix in the eggs, one at a time, until they are just combined making sure to not over-mix. Pour the cheesecake filling into the springform pan. Boil 5-6 cups of water, then pour the boiling water into the roasting pan until it is halfway up the sides of the springform pan. Bake the cheesecake for 1 hour or until it is just slightly jiggly in the middle, then turn the oven off but leave the cheesecake in the oven without opening the oven door for another 1 hour or until it is set.
After an hour, remove the cheesecake from the oven and let it cool to room temperature (about 1 hour).
Then cover springform pan with plastic wrap and place it in the refrigerator for 6-8 hours or overnight.
Before serving make the white chocolate topping. Once the cheesecake is firm, combine the cream cheese, vanilla extract, and powdered sugar with an electric mixer in a medium or large bowl until smooth. Add the melted white chocolate and blend until combined.
Slowly pour in the heavy whipping cream and continue blending until the mousse is thick and smooth. Spread the topping over the cheesecake, smooth out the top and if desired run a cake scraper with wide teeth in a circle around the top to create a patter, and place it back in the refrigerator for 1 more hour or until you are ready to serve.
Run a thin knife around the edge of the cheesecake, and carefully release the outer spring. Transfer the cheesecake to a platter or large plate and serve chilled.