Mix the chocolate wafer cookie crumbs, 2 tablespoons white sugar, and melted butter together in a bowl. Press firmly into the bottom and 1/2-inch up the sides of a 9-inch springform pan.
Bake crust in the preheated oven until set, about 8 minutes.
Beat cream cheese and 3/4 cup plus 2 tablespoons white sugar together in a bowl until creamy. Add 1 cup sour cream, eggs, and 1 teaspoon vanilla extract; beat until batter is smooth. Pour batter over crust into springform pan.
Beat 1/4 cup butter, brown sugar, and 1/4 cup white sugar together in a bowl. Stir water and 1 teaspoon vanilla extract into brown sugar mixture. Add chocolate chips and flour; stir until cookie dough is well-combined. Drop cookie dough in 2 tablespoon portions evenly over the top of the cheesecake, pushing dough beneath the surface of the batter.
Bake in the preheated oven until cheesecake is almost completely set and jiggles slightly in center when shaken, about 40 minutes.
Stir 1 cup sour cream, 2 teaspoons white sugar, and 1 teaspoon vanilla together in a bowl until smooth. Spread sour cream mixture over hot cheesecake. Cool cake to room temperature and refrigerate until cold, at least 4 hours.