Combine the softened cream cheese, sugar, and cornstarch in the bowl of a stand mixer fitted with a paddle attachment (or use a handheld mixer). Mix on medium-low speed until the mixture is creamy, like thick frosting, and no lumps of cream cheese remain. Scrape down the sides of the bowl with a spatula.
Add the sour cream and vanilla to the bowl and beat on medium-low speed until combined and creamy. Scrape down the sides of the bowl with a spatula.
Beat in the eggs and the yolk one at a time. Wait until the previous egg is just barely mixed into the batter before adding the next one.
Scrape down the sides of the bowl with a spatula. Stir the whole batter a few times by hand, being sure to scrape the bottom of the bowl, to make sure everything is incorporated. The finished batter should be thick, creamy, and silky.
Pour the cheesecake batter over the cooled crust and spread evenly. Transfer to the water bath. A cookie sheet or large roasting pan filled with 1/2"-1" hot water. At this point the spring-form pan should still have the tin foil on it. Place it all in the water on the cookie sheet (see picture in post).
Bake for 50-60 minutes. The cheesecake is done when the outer ring of the cheesecake looks slightly puffed and set, but the inner circle still jiggles (like barely set Jell-o) when you gently shake the pan.
When the cheesecake is done, turn off the oven and leave the cheesecake inside, with the door just slightly left open, and let sit and cool for 1 hour. Remove from the oven, take out of the water bath, and let cool completely on a cooling rack.
Cover and leave in the fridge for at least 12 hours, but preferrably 24 hours.
When ready to serve, cut into slices and serve with the raspberry sauce (recipe below) or whatvever topping you want.