Combine the cream and milk in a sauce pot; heat until just warm, set aside.
In a large heavy bottomed pot over medium-high heat, add the brown sugar, water and Pacific Smoke; swirl to combine. Continue to stir until the sugar is melted, dark brown and smells caramelized, 10 - 12 minutes.
Meanwhile, in a medium bowl whisk together the egg, egg yolks and cornstarch, set aside.
When the sugar is caramelized and nutty, immediately whisk in the cream mixture. The mixture will steam, froth and begin to seize, but will become smooth again as you continue whisking.
Return the mixture to a boil then lower the heat to medium.
Temper the egg mixture by whisking one cup of the hot butterscotch into the bowl of the prepared eggs and cornstarch.
Quickly whisk the egg mixture into the pot of remaining butterscotch, then boil, whisking constantly, until the custard is very thick, about 2 minutes.
Remove from the heat and whisk in the butter and rum.
Strain the custard through a fine mesh sieve, divide equally among 10 - 6 ounce serving dishes.
Cover with plastic wrap and refrigerate until completely chilled.
Serve with our Pacific Smoke salted caramel sauce (see recipe).