Lower the oven temperature to 325℉. In a large bowl or stand mixer, beat the cream cheese for 3 minutes, scraping down the sides of the bowl halfway through the beating time. Add sugar, vanilla bean paste, salt, and caramel sauce, and beat for another 3 minutes, scraping sides of the bowl periodically.
Mixing continuously, stir in first the whipping cream and then the beaten egg yolks. Stir until combined, but don’t beat for a long period of time – overbeating can incorporate air bubbles that can cause bumps in the cheesecake top. The batter will be pretty thin; this is normal.
Pour the batter evenly over the crust. Tap it on the counter a couple of times to remove any air bubbles. Transfer the foil-wrapped cheesecake into a large high-sided skillet, or a roasting pan.
Fill the baking sheet or roasting pan with hot water (hot tap water is fine) to about halfway up the side of the springform pan. Carefully place in the oven.
Bake at 325 for 60 minutes - it should be mostly set in the center and only jiggle slightly if the pan is shaken. (A bit of movement is okay; the cheesecake will continue to set as it cools. If it looks liquid-y though, bake an additional 10 minutes at a time until center appears more set.)
When the cheesecake is mostly set, turn off the oven and crack the door – leave the pan in the oven to cool and set for at least 30 minutes. (This allows the cheesecake to cool gradually; they often crack if they cool too fast.)
Remove from the water bath, and remove the foil. Cover with plastic wrap and refrigerate for at least 3 hours – or preferably overnight.