Preheat the oven to 320°F with a rack in the lower third. Line the bottom and sides of an 8-inch round cake pan (at least 3 inches deep) with parchment, letting the side strip rise about 2 inches above the rim.
Set the pan inside a larger baking pan and bring a kettle of water to a boil. Blend the cottage cheese in a blender or food processor for 2 to 3 minutes until completely silky. Transfer it to a heatproof bowl with the cream cheese and butter, set the bowl over a pot of barely simmering water and whisk until melted and perfectly smooth, about 5 minutes.
Remove from the heat and let it cool for 5 minutes. Whisk in the egg yolks one at a time, followed by the lemon juice, vanilla and salt. Sift in the cake flour and cornstarch and whisk just until smooth and glossy.
In a clean bowl, beat the egg whites with the cream of tartar on medium speed until foamy. Gradually add the sugar and keep beating until soft peaks form that curl over at the tip.
Stop before the meringue turns stiff, since an overbeaten meringue makes the cake crack and shrink. Whisk one third of the meringue into the yolk batter to lighten it. Gently fold in the remaining meringue in two additions with a spatula until no white streaks remain, then pour into the pan and tap it on the counter twice to release large bubbles.
Pour hot water into the outer pan to about 1 inch deep. Bake for 20 minutes at 320°F, then lower the oven to 285°F and bake for another 55 to 60 minutes, until tall, golden and springy to the touch.
Turn off the oven and leave the cheesecake inside with the door closed for 15 minutes, then crack the door and leave it for 15 minutes more. This slow cooling keeps it tall and fluffy.
Let it rest in the pan for 10 minutes, then gently invert onto a plate, peel off the parchment and flip it right side up onto a serving plate. Dust with powdered sugar and serve warm for a jiggly, souffle-like bite, or chill for 4 hours for a creamier texture.