Prep the pan: Line the bottom of a 9-inch springform pan with parchment and lightly grease the sides. Set your oven to 325°F (163°C).
Make the crust: In a bowl, mix graham crumbs, sugar, salt, and melted butter until the crumbs feel like wet sand.
Press firmly into the bottom and about 1 inch up the sides of the pan. Use the bottom of a measuring cup for an even layer.
Par-bake the crust: Bake for 8 to 10 minutes, until lightly fragrant. Cool on a rack while you prepare the filling.
Blend the cottage cheese: Add cottage cheese to a high-speed blender or food processor.
Blend for 1 to 2 minutes, scraping down as needed, until completely smooth and glossy. No lumps should remain.
Cream the base: In a large bowl, beat the softened cream cheese with granulated and brown sugars until silky and no streaks remain, about 2 minutes.
Combine: Beat in the blended cottage cheese until fully incorporated and smooth.
Flavor and thicken: Add vanilla, lemon zest, lemon juice, and salt. Whisk the cornstarch with the sour cream (or yogurt) until no clumps remain, then beat into the batter.
The mixture should be thick but pourable.
Add the eggs: Beat in the eggs and egg yolk one at a time on low speed, mixing just until combined. Do not overmix; too much air can cause cracks.
Fill the pan: Pour the batter over the cooled crust. Tap the pan gently on the counter a few times to release surface bubbles. Run a toothpick through any visible bubbles.
Bake low and slow: Bake at 325°F (163°C) for 45 to 55 minutes.
The edges should be set, and the center should still wobble slightly like Jell-O when you nudge the pan.
Cool gradually: Turn off the oven, crack the door, and let the cheesecake rest inside for 30 minutes. Move to a rack and cool to room temperature, about 1 to 2 hours.
Chill to set: Run a thin knife around the edge to loosen. Cover and chill for at least 6 hours, preferably overnight, before unmolding.
Serve: Unlatch the springform, remove the ring, and slide the cheesecake onto a platter.
Top with lemon curd, berries, or whipped cream if you like. Slice with a hot, clean knife for neat wedges.