Melt the butter in a medium-sized saucepan. Add the dark brown sugar and salt, then stir until the sugar is well-moistened. Remove from heat.

In a small bowl, whisk together the cornstarch with about ¼ cup (60ml) of the half and half until smooth and lump-free. Then whisk in the eggs.

Combine the remaining half and half with the cornstarch mixture and pour into the melted brown sugar, whisking continually.

Return the pan to the heat and bring the mixture to a foil whisking frequently. Once it begins to bubble, reduce the heat to a low simmer and continue to cook for one minute, whisking non-stop, until the pudding thickens. It will be similar to the consistency of hot fudge sauce.

Remove from heat and stir in the rum (if using) and vanilla.

Pour into 4-6 serving glasses or custard cups or dessert bowls and chill thoroughly, at least four hours, before serving. I like to bring the pudding back to room temperature before serving with a topping of Caramelized Apples and a dollop of freshly whipped cream.