Heat the oven to 390°F/200°C, conventional setting. Set a wide roasting pan on the lower third of the oven and fill halfway with boiling water.
Separate the eggs. In a large bowl, whisk the cheese, sour cream, heavy cream, half the sugar, egg yolks, and vanilla until smooth. Sift in the cornstarch and pudding mix and whisk until fully incorporated.
In a stand mixer fitted with the whisk attachment, beat the egg whites on medium speed until foamy. Gradually add the remaining sugar and whip to glossy, firm peaks.
Fold half the meringue into the cheese mixture, then gently fold in the remainder until smooth.
Generously butter a 9-inch/22 cm deep round pan or jachnun pot and line the bottom with parchment. Pour in the batter, smooth the top, tap gently to release air bubbles, and wrap the sides with aluminum foil.
Set the pan in the water bath and bake for 25 to 30 minutes, until lightly golden. Reduce the temperature to 310°F/155°C and bake for 70 minutes.
Turn off the oven and leave the cake inside, door closed, for 2 to 3 hours. Refrigerate overnight.
Run a knife around the edge, unmold, invert onto a serving platter, and dust with powdered sugar.