Preheat the oven to 350°F (176°C), line the bottom of a 9-inch springform pan with parchment, and grease the sides. Cream butter and sugar together for 3–4 minutes until pale and fluffy. Blend in sour cream and vanilla extract. Mix in egg whites thoroughly. In another bowl, whisk together the flour and baking powder. Incorporate half of the dry mixture into the batter, then add the milk and water, mixing well. Blend in the remaining dry ingredients until smooth. Evenly distribute the batter in the pan and bake for 18–20 minutes, or until a toothpick yields a few moist crumbs. Let the cake cool.
While the cake cools, place chocolate chips in a bowl. Bring cream to a boil, pour over chips, add vanilla, sit 3–4 minutes, then whisk smooth and set aside. Beat cream cheese, sugar, and flour at low speed until smooth. Mix in sour cream and vanilla on low. Add eggs one by one, mixing gently. Lower oven to 300°F (148°C) once the cake cools. Detach, clean, and re-grease the pan sides. Reassemble with cake at the base. Spread chocolate ganache over cake, staying half an inch from the edge. Pour in cheesecake filling, starting at the edges. Wrap pan in foil and set it in a water bath in a larger pan. Fill halfway up with hot water, avoiding overflow.
Bake for 1 hour 15 minutes; the center should jiggle slightly. Turn off oven, leave door shut for 30 minutes, then crack door for 30 more minutes to cool slowly. Remove, unwrap, and chill 5–6 hours or overnight until firm. Release from pan.
For toppings, place chocolate chips in a bowl. Heat cream to boiling, pour over chips, add corn syrup and vanilla, let sit, then whisk smooth. Refrigerate until cooled. For pastry cream, lightly beat egg yolks in a bowl. Mix sugar, cornstarch, and milk in a saucepan until smooth. Cook over medium-high heat until bubbling and thick. Simmer 2 minutes, remove from heat. Temper egg yolks with a bit of hot milk mixture, then return all to pan. Boil lightly for 2 minutes with stirring. Remove from heat, stir in butter and vanilla, cover, and chill completely.
To assemble, pipe chocolate ganache around cheesecake's edge using a fitted piping bag. Fill center with pastry cream and smooth out. Cover and refrigerate until serving. Best enjoyed within 2–3 days.