Heat the oven to 350°F with a rack in the lower-middle position. Grease a 9-inch springform pan, line the bottom with parchment, wrap the outside bottom with foil and set it on a rimmed sheet pan.
Stir graham crumbs, 2 tablespoons sugar and 1/4 teaspoon salt. Mix in melted butter, press evenly over the pan bottom and bake 8 minutes. Cool at least 10 minutes and reduce the oven to 325°F.
Blend cottage cheese, Greek yogurt, 3/4 cup sugar, cornstarch, lemon zest, lemon juice, vanilla and 1/4 teaspoon salt for 60 to 90 seconds, scraping once, until glossy and completely curd-free.
On the lowest speed, add eggs one at a time and mix only until each disappears. Let an overly bubbly batter stand 5 minutes and skim the largest bubbles.
Pour batter over the cooled crust. Tap the pan gently two or three times and pop large surface bubbles with a toothpick.
Bake at 325°F for 50 to 65 minutes, until the outer 2 inches are set and a 2- to 3-inch circle in the center moves as one soft unit when nudged.
Turn off the oven, crack the door and leave the cheesecake inside 30 minutes. Cool on a rack about 1 hour, running a thin knife around the edge after the first 15 minutes.
Cover and refrigerate at least 6 hours, preferably overnight. Remove the springform ring only when the cheesecake is fully cold.
Dip a thin sharp knife in hot water, wipe dry and cut. Clean and warm the blade between slices; let slices stand 10 minutes before serving.
