In a sturdy, medium-sized saucepan (I used a steel one), combine the butter and brown sugar. Set it on low heat and use a silicone spatula or wooden spoon to stir constantly as the butter and sugar melt down together.
See photos below. The butter will initially separate from the sugar because of the acid in brown sugar. Keep stirring and it will come together, continuing to have a glossy appearance. Don't take your eyes off the pan, because caramel cooks pretty quickly!
Once the caramel starts to smoke a bit (after about 3 minutes), it's done and will have a slightly bitter flavour which prevents the drink from being too sweet. You can turn it off at this point, or let it darken for a few more seconds till it starts to smell just a little of burnt sugar, for a more bittersweet end result, which is what I prefer. Don't forget to stir continuously.
Take the pan off the heat, and carefully add the cream because it will splutter and foam (last photo below). Then put the pan back on low heat and pour in the milk in a slow stream, stirring all the while. The caramel may start to solidify a little (all the more reason the milk should be at room temp), but whisk it with a balloon whisk and it will dissolve again.
Let the mixture come to a low boil. The milk would have darkened considerably. If it looks too thick, feel free to add more milk to bring it to the consistency you prefer. Pour into one large or two small cups (it's a rich drink and I do think two people can happily share!), top with whipped cream if you like. Enjoy immediately! You can store it in the fridge for a day or two, reheating as needed.