Preheat oven to 350 degrees F (175 degrees C). Grease a 9-inch springform pan.
Combine cookie crumbs, confectioners' sugar, and cocoa powder in a large bowl. Add melted butter; stir until well mixed. Pat mixture into the bottom of the prepared pan.
Bake in the preheated oven until crust is set, about 10 minutes.
Beat cream cheese and white sugar together until well blended. Add eggs, 1 at a time, mixing well after each addition. Blend in sour cream and vanilla extract; mix on low speed.
Pour half-and-half into a saucepan over medium-low heat. Cook until mostly heated through, about 2 minutes. Add caramel candies a few at a time and cook, stirring frequently, until smooth, about 5 minutes. Pour caramel mixture into the cream cheese mixture; mix on low speed until well blended. Pour filling over the baked crust.
Melt chocolate in a microwave-safe bowl in 15-second increments, stirring after each melting, 1 to 3 minutes. Drizzle over the filling; drag a knife through the filling to make a marbled effect. Fill a rimmed baking sheet with water and place on the bottom rack of the oven.
Bake cake in the preheated oven until set, about 55 minutes. Turn heat off and let cheesecake cool in the oven for 45 minutes. Cover with plastic wrap and refrigerate for at least 6 hours.