In the bowl of a stand mixer and using the paddle attachment, blend together the cream cheese and sugar until smooth. (Low speed.) Scrape sides and bottom of bowl as needed.
Add the eggs and blend on low speed until incorporated.
Add the lemon zest, lemon juice, and vanilla extract. Scrape sides and bottom of bowl and the paddle attachment. The zest has a tendency to collect on the paddle. Give the ingredients a quick stir to make sure that everything is well distributed.
Pour on top of the crust. (Note: If baking with a decorative fruit puree topping, please see directions below.) Bake for 20-25 minutes until filling is set. It is okay if the middle jiggles just slightly. I like to do the toothpick test, though. Insert a toothpick in the middle of the filling. The toothpick will have some of the filling clinging to it, however the filling should not look liquid on the toothpick. If the filling has cooked properly, there will be little moist bits of it clinging to the toothpick.
Remove from oven and allow to cool completely. Cover and refrigerate for at least an hour, then cut into squares. I cut the cheesecake into 24 squares.