Preheat your oven to 325°F (160°C).

In a mixing bowl, combine chocolate graham cracker crumbs, melted butter, and ¼ cup sugar. Press mixture firmly into the bottom of a 9-inch springform pan. Bake for 10 minutes, then cool while preparing filling.

Beat softened cream cheese until completely smooth, about 2 minutes. Gradually add 1 cup sugar and beat until well combined. Add eggs one at a time, mixing gently after each addition. Mix in vanilla extract.

Divide filling equally into three separate bowls. Stir melted dark chocolate and about 2.5 tablespoons sour cream into the first bowl until smooth. Repeat with milk chocolate and sour cream in the second bowl and white chocolate with remaining sour cream in the third bowl.

Pour dark chocolate filling into cooled crust and spread evenly. Carefully pour milk chocolate filling over the back of a spoon onto the dark layer, then smooth. Finally, add white chocolate layer on top.

Bake for 55-60 minutes until center is set but still jiggles slightly when gently shaken.

Turn off oven and let cheesecake sit inside with door slightly ajar for 1 hour. Remove and cool to room temperature.

Refrigerate for at least 4 hours or overnight. Before serving, garnish with whipped cream and chocolate shavings.