In a medium saucepan, heat 2 cups of heavy cream over medium heat until it begins to simmer, around 5 minutes. Stir in ¾ cup of brown sugar and mix until fully dissolved. Remove from heat and let cool for a few minutes.

In a separate bowl, whisk together 5 large egg yolks and 1 teaspoon of vanilla extract until well blended and slightly frothy. Slowly incorporate the warm cream mixture into the egg yolks, whisking continuously.

Once combined, add 2 tablespoons of dark rum and a pinch of sea salt to the custard mixture. Stir gently to incorporate these flavors.

Preheat your oven to 325°F (160°C). Pour the custard mixture into individual ramekins, filling them about three-quarters full. Place in a baking dish, and carefully fill the dish with hot water until halfway up the sides. Bake for 30-35 minutes.

Remove the ramekins from the water bath and let cool at room temperature for about 30 minutes. Cover with plastic wrap and refrigerate for at least 4 hours, preferably overnight.

Prior to serving, sprinkle a thin layer of brown sugar over the chilled custards. Caramelize the sugar with a kitchen torch until it melts and turns golden brown.

Let the Caribbean Creme Brûlée cool for a minute before serving, allowing the sugary top to harden.