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 1/4 cup (60ml) of the milk until smooth (there should be no visible pills of cornstarch), then whisk in the eggs.
Gradually pour the remaining milk into the melted brown sugar, whisking constantly, then whisk in the cornstarch mixture as well.
Return the pan to the heat and bring the mixture to a boil, 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 to the consistency of hot fudge sauce.
Remove from heat and stir in the Bourbon and vanilla. If slightly-curdled looking, blend as indicated above.
Pour into 4-6 serving glasses or custard cups and chill thoroughly, at least four hours, before serving.