"Every time I make this cheesecake people think I bought it from the Cheesecake Factory. It truly is an amazing recipe that people will just go gaga over. I like to decorate with prepared cream cheese frosting and raspberries (the raspberries add a nice complementary flavor)."
Mix cookie crumbs and butter together in a bowl. Press crust mixture into a 9-inch springform pan.
Beat cream cheese, eggs, sugar, and vanilla extract together in a large bowl with an electric mixer until smooth and fluffy. Spoon 1/2 of the cream cheese mixture into the crust.
Break dark chocolate and milk chocolate into smaller pieces. Place dark chocolate and 1/4 of the milk chocolate in the top of a double boiler over simmering water. Stir frequently, scraping down the sides with a rubber spatula to avoid scorching, until chocolate is melted, about 5 minutes.
Stir melted chocolate into the bowl of remaining cream cheese mixture. Drizzle over the batter in the crust to make a swirl pattern.
Bake in the preheated oven until center is set, about 50 minutes. Transfer cheesecake to a wire rack to cool cheesecake completely, at least 40 minutes.
Place the cheesecake on a serving plate. Cover with plastic wrap and refrigerate until chilled, 2 hours to overnight.
Melt the remaining milk chocolate using the double broiler, about 5 minutes. Combine with sour cream in a small bowl; spread over the cheesecake. Chill until frosting is set, about 5 minutes.