Mix cream cheese, goat cheese, sugar, salt, and corn starch using paddle attachment on medium speed, scraping sides of bowl after about 30 seconds. Mix for another minute or so until well combined.
Add in sour cream, lemon zest, and vanilla and continue to mix for another minute until combined. Scrape paddle and bowl well.
With mixer on medium, add eggs, 1 at a time, mixing until just combined, scraping sides halfway through. Careful not to over mix/whip after the eggs are added.
Pour mixture into fully cooled crust shell.
Bake at 325°F/160°C for 60 minutes. At this point, the cheesecake should have risen and still be jiggly in the center. Turn off oven and allow to cool in the oven, door closed for 45 minutes.
Remove from the oven and allow to come to room temperature.
Tent with foil and refrigerate for at least 10 hours.