In a large saucepan over medium-low heat, combine light brown sugar, 1/4 cup of water, and a pinch of salt. Stir gently and swirl the pot until the mixture begins to boil.

While the caramel cools, whisk together 1 cup of half-and-half, 3 egg yolks, and 2 tablespoons of cornstarch until smooth. Set aside.

Gradually pour the cooled caramel into the dairy mixture while whisking consistently to blend.

Return the combined mixture to the saucepan over medium-low heat, continuously whisk until thickened, about 5-7 minutes.

Remove from heat and stir in 2 tablespoons of butter, dark rum or bourbon, and 1 teaspoon of vanilla extract.

Strain the mixture through a fine mesh strainer into a clean bowl or pitcher for an ultra-smooth texture.

Pour the strained mixture into individual ramekins, cool slightly, then cover and refrigerate for at least 2 hours.

Before serving, drizzle thick caramel sauce over the top and sprinkle with coarse sea salt.