Preheat your oven to 325°F (160°C). Grease the bottom and sides of a 9-inch springform pan with butter or cooking spray. Place the pan on a baking sheet to catch any drips.
In a mixing bowl, combine the graham cracker crumbs, melted butter, and granulated sugar. Stir until the mixture resembles coarse crumbs and is well combined. Press the mixture firmly into the bottom of the prepared springform pan to form an even crust.
In a separate mixing bowl, combine the softened cream cheese, sugar, and vanilla extract. Beat with an electric mixer or whisk until smooth and creamy. Add the eggs, one at a time, mixing well after each addition. Finally, add the plain yogurt and lemon zest (if using), and mix until all ingredients are fully incorporated.
Pour the filling mixture over the crust in the springform pan. Smooth the top with a spatula. Place the baking sheet with the pan in the preheated oven and bake for 50-60 minutes, or until the edges are set and the center is slightly jiggly. The cheesecake will continue to firm up as it cools.
Once baked, remove the cheesecake from the oven and let it cool to room temperature on a wire rack. Once cooled, cover the springform pan with plastic wrap or aluminum foil and refrigerate for at least 4 hours or overnight to allow the cheesecake to set.
When ready to serve, carefully remove the sides of the springform pan. Slice the baked yogurt cheesecake into desired portions and serve chilled. Garnish with fresh fruits, berry compote, or a dusting of powdered sugar if desired.