Preheat oven to 350 degrees F and position lower rack in the oven.
Prepare a 9-inch springform pan by greasing well with butter. Wrap foil tightly around the outside of the pan to block water from the water bath from getting in. Make sure there are no holes.
To make the crust, mix sugar and butter together with a hand mixer until light and fluffy. About 2-3 minutes. Then add in the egg, whole milk, vanilla extract and lemon zest.
In a separate bowl, combine cake flour, baking powder and salt. Stir into wet ingredients until combined.
Spoon batter into the pan and bake for 15 minutes until just brown along the edges. Let cool in the pan while you make the cheesecake.
In a large bowl, use a hand mixer to whip cream cheese and sugar together until smooth. Then mix in sour cream and then milk. Then mix in eggs one at a time just until combined.
Stir in vanilla and lemon zest and then stir in flour until combined.
Pour half of the batter into the prepared pan over cooled crust, and then add cooled melted chocolate to the other half and incorporate. Pour remaining batter over the vanilla layer making sure batter should not reach the top of the pan. Place the foil-wrapped pan in a large roasting pan with high sides. Pour boiling water until it reaches halfway up the cheesecake pan to make a water bath.
Place on the lower rack and bake for 1 hour. You can also pour the boiling water in the pan after the cheesecake is set up in the oven in the roasting pan. Either way, don’t burn yourself!
Bake in preheated oven for 1 hour. Turn the oven off, and let cake cool in oven with the door closed for 5 hours to prevent cracking. Then chill in the refrigerator overnight, or at least 4 hours.
To make the icing, mix together confectioner’s sugar, corn syrup, lemon juice, vanilla and water. Transfer half of the icing to another bowl and add cocoa powder. Add more water if needed to get desired consistency. Frost as desired and chill cheesecake in the refrigerator until frosting is set and you are ready to serve (at least 1 hour).