Preheat the oven to 325°F (160°C). While it's heating, blend the cottage cheese in a food processor or high-powered blender until smooth and creamy. This step is crucial to getting that silky cheesecake texture.
Add the Greek yogurt, eggs, honey (or sugar), vanilla extract, cornstarch, and lemon zest (if using) to the blender with the cottage cheese. Blend again until everything is thoroughly combined and smooth. Make sure no lumps remain!
Prepare the crust: If using a store-bought graham cracker crust, simply set it aside. If making your own, combine the crushed graham crackers, melted butter, and sugar. Press the mixture firmly into the bottom of a 9-inch springform pan or pie dish, then bake for 10 minutes to set.
Pour the filling into the prepared crust, smoothing out the top with a spatula. Give the pan a few taps on the counter to remove any air bubbles.
Bake the cheesecake for 45-50 minutes, or until the edges are set but the center still has a slight jiggle. Don't worry, it will firm up as it cools.
Cool completely at room temperature before transferring to the refrigerator. Chill for at least 4 hours, but overnight is best for the flavors to develop.