Pour the milk and cream into a saucepan and bring to a simmer.
Take off the heat and cover so it stays warm.
Bring 1/3 cup of water, the brown sugar and salt to a boil in a pot.
Cook the mixture, stirring frequently, for 10 minutes or until it gets to 240°F on your candy thermometer.
Whisk the brown sugar mixture with the cream mixture as soon as it reaches that temperature.
Bring the pudding to a boil, whisking all the time, until it’s smooth.
Next, whisk the whole egg, egg yolks and cornstarch.
Whisk a ladleful of the cream mixture into the egg mixture, and keep whisking so the eggs don’t curdle.
Now, pour the egg mixture into the pan with the warm cream, whisking all the time and cooking for 3 minutes or until thick.
Strain the pudding into a glass bowl, then whisk in the butter until the custard is smooth.
Divide it between serving dishes and refrigerate for 4 hours at least, or until the custard has set.