In a medium saucepan, combine light brown sugar, water, and a pinch of salt over medium-low heat. Stir until the mixture boils and the sugar dissolves, about 5-6 minutes.

While the caramel cools, whisk together half and half, egg yolks, and cornstarch in a medium mixing bowl until smooth and free of lumps.

Once the caramel has cooled slightly, gradually whisk the pudding base into the caramel mixture until well incorporated.

Return the mixture to the saucepan over medium-low heat, whisking continuously. Cook for about 5-10 minutes until the pudding thickens.

Remove from heat and stir in butter, dark rum or bourbon, and vanilla extract. Strain through a mesh sieve into serving vessels.

Allow to cool for a few minutes before covering and refrigerating for at least 2 hours to set.

Before serving, drizzle with salted caramel and sprinkle sea salt on top. Serve in individual ramekins.