Add the sugar to a saucepan and heat over medium heat until sugar melts. Stir constantly to prevent burning.
Add the butter and stir until it melts.
Add the cream slowly, continuing to stir.
Remove from heat and add salt and vanilla. Mix until thoroughly combined.
Set caramel aside to cool to room temperature.
Preheat oven to 350 degrees.
Pulse graham crackers in a food processor.
Add the brown sugar and mix.
Add melted butter and mix thoroughly
Lightly spray springform pan with cooking spray.
Press graham cracker mixture into the bottom and sides of pan.
Bake the crust for 10 minutes. Set aside and allow to cool completely.
Beat the cream cheese until smooth and creamy.
Add brown sugar and granulated sugar and beat until well combined. Scrape the side of the bowl, as needed.
Add sour cream and beat until well combined.
Add the eggs , one at a time and mix until just combined, without over-mixing.
Add the vanilla and salt and lightly mix to combine.
Pour half of the batter into the prepared crust.
Pour half the caramel over the batter and use a knife to swirl the caramel.
Add the remaining batter and smooth with a spoon or offset knife.
Wrap the bottom of the springform pan with foil, to avoid accidental leaks.
Place foil-lined pan in a roasting pan and add water to the pan to create a bain-marie (water bath).
Bake the cheesecake at 325 degrees for 60-75 minutes, until cake sides are set. Middle of the cake will still be a little wiggly.
Turn off the oven, but leave the cake in the oven for about 45 minutes.
Remove cake from oven and refrigerate for 4-6 hours.
Just before serving, pour remaining caramel over the top and smooth with an offset knife.
Refrigerate for another 20-30 minutes in order for caramel to firm up.
Sprinkle sea salt flakes across the edges of the cake (optional).