In a large saucepan, combine light brown sugar, water, and salt. Swirl gently and heat until it boils. Cook for 5-6 minutes until amber, then cool slightly.

In a mixing bowl, whisk together half and half, egg yolks, and cornstarch until smooth.

Gradually add the cream mixture to the caramel, whisking vigorously. Return to low heat and whisk for 8-10 minutes until thickened.

Remove from heat and stir in butter, dark rum or bourbon (if using), and vanilla extract.

Strain the mixture into bowls or jars, cool at room temperature, then refrigerate for at least 2 hours.