Combine cookie crumbs and butter in a medium bowl; press mixture into bottom and 1 inch up sides of a 9-inch springform pan. Set aside.
Place white chocolate morsels in top of a double boiler; bring water to a boil. Reduce heat to low; cook until chocolate melts, about 5 minutes. Pour into a small bowl; cool slightly.
Place semisweet morsels in top of a double boiler; bring water to a boil. Reduce heat to low; cook until chocolate melts, about 5 minutes. Pour into a small bowl; cool slightly.
Beat cream cheese at medium speed with an electric mixer until creamy; gradually add sugar, beating well. Add eggs, 1 at a time, beating until blended after each addition. Stir in whipping cream, vanilla, and salt.
Remove 1 cup batter; stir into melted semisweet chocolate until combined.
Stir melted white chocolate into remaining batter; pour batter into prepared crust.
Spoon reserved chocolate batter by rounded tablespoons onto white chocolate batter; swirl with knife to create a marbled effect.
Bake at 350° for 30 minutes. Reduce heat to 250°; bake 1 hour and 10 minutes or until cheesecake is almost set. Run a knife around edge of pan, and release sides. Cool completely in pan on a wire rack; cover and chill 8 hours. Store in refrigerator.
Tip: If you don't have a double boiler, place the chocolate morsels in a microwave-safe bowl, and microwave at HIGH 1 minute, stirring once, until chocolate melts.