Preheat the oven to 350°F and wrap the outside of a 9-inch springform pan with two layers of heavy-duty foil. Stir together the graham cracker crumbs, sugar, salt and melted butter, then press the mixture firmly into the bottom of the pan.Bake the crust for 10 minutes and let it cool while you make the filling. Reduce the oven to 325°F and bring a kettle of water to a boil.
Add the cottage cheese to a food processor or blender and blend for 2 to 3 minutes, scraping down the sides, until it is completely silky with no curds left. This step is what gives the cheesecake its smooth, dense New York texture.
Add the cream cheese, Greek yogurt, sugar, cornstarch, lemon juice, lemon zest, vanilla and salt, then blend for about 1 minute until smooth and glossy.Add the eggs and pulse just until combined, about 5 to 6 pulses. Overmixing whips in air, which can cause cracks.
Pour the filling over the cooled crust and tap the pan on the counter a few times to release air bubbles. Set the springform in a large roasting pan and pour hot water into the roasting pan until it reaches about 1 inch up the sides.Bake for 60 to 70 minutes, until the edges are set and the center still wobbles slightly when you gently nudge the pan.
While the cheesecake bakes, whisk together the Greek yogurt, powdered sugar and vanilla for the topping. When the cheesecake is done, gently spread the topping over the hot surface and return it to the oven for 8 more minutes.
Turn off the oven, crack the door open and let the cheesecake cool inside for 1 hour. Lift it out of the water bath, remove the foil, run a thin spatula around the edge to loosen it and let it cool completely at room temperature.
Refrigerate the cheesecake for at least 8 hours or overnight so it sets firm and the flavor develops. Release the springform ring, slice and serve cold.