In a 2 to 3 quart sized saucepan, whisk together the brown sugar, cornstarch, and salt until evenly coloured. Slowly whisk the milk and egg yolks together and slowly drizzle the egg mixture into the pan holding the sugar mixture while whisking briskly. Place the pan over medium heat and whisk constantly while bringing to a boil. When it reaches the boil, drop the heat to LOW and stir constantly for 1 minute, or until thickened and the whisk leaves ribbony marks behind it as you stir. Remove from the heat and pour through a fine mesh sieve into a heat proof bowl or large measuring cup. Stir in the butter and vanilla until the butter is fully melted.