Prep the pan. Line the bottom of a 9-inch springform pan with parchment and lightly grease the sides. Wrap the outside of the pan in two layers of heavy-duty foil to protect it from water in the bath.
Make the crust. In a bowl, mix graham cracker crumbs, sugar, and salt. Stir in melted butter until the crumbs feel like wet sand. Press firmly into the bottom and slightly up the sides of the pan. Bake at 350°F (175°C) for 8–10 minutes. Cool while you make the filling.
Lower the oven temperature. Reduce to 325°F (165°C). Bring a kettle of water to a boil for the water bath.
Blend the filling gently. With a mixer on low to medium-low, beat cream cheese until smooth, about 2 minutes. Add sugar and salt, mix until combined. Blend in sour cream, heavy cream, and vanilla. Add eggs one at a time, mixing just until incorporated. Do not overmix—too much air causes cracks.
Assemble for baking. Pour filling over the cooled crust. Place the foil-wrapped pan in a large roasting pan. Pour hot water into the roasting pan to reach halfway up the sides of the springform pan.
Bake. Bake at 325°F (165°C) for 55–70 minutes. The edges should be set and slightly puffed, and the center should jiggle like set Jell-O. Don’t wait for it to be firm in the middle.
Cool slowly. Turn off the oven, crack the door, and let the cheesecake rest inside for 45–60 minutes. Remove from the water bath, run a thin knife around the edge, and cool to room temperature. Chill at least 6 hours, preferably overnight.
Make the salted caramel. In a heavy saucepan, heat sugar over medium heat, stirring just until it starts to melt, then stop stirring. Swirl the pan as the sugar turns deep amber. Add butter carefully (it will bubble), whisk until smooth. Slowly stream in warm cream, whisking constantly. Remove from heat and stir in vanilla and flaky sea salt to taste. Let cool to a pourable but thick consistency.
Top the cheesecake. Pour a layer of caramel over the chilled cheesecake and gently tilt to spread. Chill 20–30 minutes to set. Sprinkle a touch more flaky sea salt before serving, if you like.
Slice cleanly. Use a sharp knife warmed in hot water and wiped dry between cuts for neat slices.