Step 1: Preheat your oven to 325°F (163°C) and grease a 9-inch springform pan. Wrap the outside of the pan in double layers of heavy-duty aluminum foil to prevent water from leaking in during the water bath.
Step 2: Combine Graham cracker crumbs, melted butter, and brown sugar in a medium bowl. Press the mixture firmly into the bottom of the prepared pan. Bake for 10 minutes, then set aside to cool.
Step 3: In a large bowl, beat the room-temperature cream cheese and granulated sugar together on medium-low speed until smooth and creamy. Do not overmix to avoid air bubbles.
Step 4: Add the sour cream and vanilla extract, mixing until just combined. Add eggs one at a time, beating on low speed after each addition until just incorporated.
Step 5: Pour the cheesecake batter over the cooled crust. Place the springform pan into a larger roasting pan and fill the roasting pan with hot water until it reaches halfway up the sides of the springform pan.
Step 6: Bake for 70-75 minutes or until the edges are set and the center has a slight jiggle. Turn off the oven, crack the door, and let the cheesecake cool inside for 1 hour.
Step 7: Remove from the water bath and chill in the refrigerator for at least 6 hours, preferably overnight.
Step 8: To make the caramel, melt 1 cup of sugar in a saucepan over medium heat, stirring constantly until it turns a deep amber color. Carefully whisk in 6 tbsp of butter until melted.
Step 9: Slowly pour in the heavy cream while whisking (it will bubble up). Let it boil for 1 minute, then remove from heat and stir in the sea salt. Let the caramel cool to room temperature.
Step 10: Pour the cooled caramel over the chilled cheesecake before serving. Slice with a warm knife for clean edges.