Step 1: Preheat your oven to 350°F (175°C). Lightly grease a 9-inch springform pan. In a medium bowl, combine 1½ cups crushed graham cracker crumbs, ¼ cup granulated sugar, and 6 tablespoons melted unsalted butter. Mix until well combined. Press the mixture firmly into the bottom of the prepared springform pan. Bake for 10-12 minutes, until lightly golden. Remove from oven and let cool completely on a wire rack.
Step 2: In a heavy-bottomed saucepan, combine 1 cup granulated sugar and ¼ cup water. Cook over medium-high heat without stirring, gently swirling the pan occasionally, until the sugar dissolves and the syrup turns a deep amber color. This takes about 8-10 minutes.
Step 3: Carefully and slowly pour ½ cup warm heavy cream into the hot caramel (it will bubble up aggressively). Stir gently with a heatproof spatula until smooth. Remove from heat and stir in 4 tablespoons unsalted butter and ½ teaspoon sea salt. Continue stirring until the butter is fully melted and incorporated. Let cool completely before using.
Step 4: Reduce oven temperature to 325°F (160°C). In a large bowl, using an electric mixer on medium speed, beat 32 ounces full-fat cream cheese (softened) until completely smooth, about 2-3 minutes. Scrape down the sides of the bowl.
Step 5: Gradually add 1½ cups granulated sugar, beating until just combined and smooth. Do not overmix. Beat in 1 teaspoon vanilla extract. Then, add ½ cup sour cream and ¼ cup heavy cream, beating until just incorporated.
Step 6: Add 4 large eggs, one at a time, beating on low speed until just combined after each addition. Do not overmix.
Step 7: Gently fold in ¾ cup of the cooled salted caramel sauce (reserving the rest for topping). Pour the cheesecake filling over the cooled crust in the springform pan.
Step 8: Prepare a water bath: wrap the bottom and sides of the springform pan tightly with several layers of heavy-duty aluminum foil to prevent water from seeping in. Place the foiled pan into a larger roasting pan. Carefully pour hot water into the roasting pan until it reaches halfway up the sides of the springform pan.
Step 9: Carefully transfer the roasting pan to the preheated oven. Bake for 1 hour to 1 hour 15 minutes, or until the edges are set, but the center 2-3 inches still jiggles slightly when gently shaken.
Step 10: Turn off the oven, crack the door open slightly, and leave the cheesecake in the water bath for 1 hour to cool slowly. Remove from oven and water bath, unwrap foil, and let cool completely on a wire rack. Then, cover loosely with plastic wrap and refrigerate for at least 6 hours, or preferably overnight, for the ultimate silky texture.
Step 11: Once chilled, carefully remove the sides of the springform pan. Drizzle generously with the remaining cooled salted caramel sauce. A sprinkle of flaky sea salt before serving enhances the flavors.