Lightly butter the sides and bottom of a 9-in. springform pan.
To prepare the crust, mix together the sugar, crumbs and butter. Cover only the bottom of the prepared pan with the crumb mixture, using your fingers to press the mixture into an even layer.
To prepare the cheesecake, beat the cream cheese on medium-high speed in the bowl of an electric mixer fitted with a flat paddle.
Add the sugar and vanilla and beat until the mixture is light and creamy. Scrape the inside surface of the bowl. Beat 30 seconds more. Add the flour and mix to incorporate.
Reduce the speed to low, add the eggs one at a time and mix to incorporate after each addition. Do not overmix the batter once the eggs have been added.
Divide the batter evenly into 3 separate bowls, about 2 1/2 c. each.
Add the chopped pecans and chocolate chips to one bowl and mix to incorporate. Pour this batter over the crust layer and spread the batter into an even layer. Place the pan in the freezer for 60 - 70 minutes or until the cheesecake layer is firm.
Preheat the oven to 325°F/160°C.
Add the melted chocolate and Kahlua to the second bowl of batter and beat until evenly incorporated. Pour this batter over the pecan layer and spread into an even layer. Return the pan to the freezer for 40 - 45 minutes, or until firm.
Pour the remaining vanilla batter over the chocolate layer and spread into an even layer.
Wrap the bottom of the pan in a double layer of aluminum foil and place the pan in a large roasting pan. Place the pan on the middle shelf of the oven. Carefully pour hot water into the roasting pan. The water should rise halfway up the sides of the springform pan.
Bake the cheesecake for 1 hour and 20 minutes to 1 hour and 25 minutes. The cake should be slightly soft in the center. Remove the springform pan from the roasting pan and remove the aluminum foil. Transfer the cake to a wire rack and cool at room temperature for 1 hour.
Chill the cake for 1 hour and then remove the sides of the springform pan. Cover with plastic wrap and chill several more hours or overnight.
Garnish with fudge sauce if desired. Slice and serve.