Split 1 vanilla bean lengthwise with the tip of a sharp knife. Holding the pod open, scrape seeds from each half using the flat side of your knife; place in a bowl. Repeat with second vanilla bean, placing seeds in a separate bowl.
Preheat oven to 350 degrees F (175 degrees C).
Mix graham cracker crumbs, melted butter, and 1/4 white sugar together in a bowl. Press over the bottom and up the sides of a 9-inch springform pan.
Combine 2 packages cream cheese, sour cream, 1 cup white sugar, and cornstarch in a large bowl; mix until sugar is dissolved. Add seeds from 1 vanilla bean, softened butter, and vanilla extract; blend until smooth. Pour over graham cracker crust.
Bake in the preheated oven until top is a light tan color, 30 to 35 minutes. Cool for 1 to 2 hours.
Beat 2 cups heavy cream in a chilled bowl with an electric mixer until soft peaks form. Add 1/4 confectioners' sugar, 1 tablespoon at a time, beating until cream is stiff. Place in the refrigerator.
Melt white chocolate in top of a double boiler over simmering water, stirring frequently and scraping down the sides with a rubber spatula to avoid scorching. Remove from heat and let cool, about 5 minutes.
Beat 1 package cream cheese with an electric mixer until fluffy. Beat in white chocolate until smooth. Fold in whipped cream. Spread over the cooled cheesecake. Chill for 1 to 2 hours.
Beat 1 cup heavy cream in a chilled bowl with an electric mixer until soft peaks form. Beat in seeds from the second vanilla bean and 1 1/2 tablespoon confectioners' sugar until stiff peaks form. Spread over cheesecake. Cover and refrigerate until firm, at least 1 day.
