In a stand mixer fitted with the whisk attachment, beat the softened cream cheese on medium-low speed until it’s velvety smooth, about 2 minutes. Gradually add the sugar and salt, continuing to mix until everything is well incorporated, pausing occasionally to scrape down the sides. Next, blend in the sour cream, lemon zest, and vanilla extract, mixing for about 1 minute until the mixture is fully combined. After scraping the bowl once more, add the lightly beaten eggs, and mix on low speed just until they are fully incorporated. Pour the filling over the cooled crust, filling the pan to the top.