Preheat oven to 325°F (163°C). Lightly grease a 9-inch springform pan, line the bottom with parchment paper, and place on a rimmed baking sheet.
Mix graham cracker crumbs, sugar, and melted butter until moistened. Press firmly into the bottom of the pan. Bake for 8-10 minutes until lightly golden, then cool completely.
Beat softened cream cheese on medium speed for 2 minutes until smooth and fluffy. Scrape down the bowl thoroughly.
Add sugar and cornstarch to the cream cheese and mix on low until incorporated, about 1 minute. Scrape down the bowl again.
Add Greek yogurt, vanilla extract, lemon juice, and lemon zest. Mix on low just until combined, about 30 seconds.
Add eggs and egg yolk one at a time, mixing on the lowest speed after each addition just until incorporated. Fold gently with a spatula to ensure even mixing.
Pour filling over the cooled crust and smooth the top. Tap the pan on the counter 3-4 times to release air bubbles.
Bake for 50-60 minutes until edges are set and center has a gentle jiggle (about the size of a tennis ball). Do not open the oven door for the first 40 minutes.
Turn off the oven and leave the cheesecake inside with the door cracked open for 1 hour. Then run a knife around the edge and cool completely on a wire rack.
Cover loosely with plastic wrap and refrigerate for at least 6 hours, preferably overnight. Release the springform pan and serve chilled with your choice of toppings.