Combine the heavy cream and milk and set aside.
In a large, heavy-bottomed pot over medium high heat, stir the brown sugar, a half cup of water and the salt. Cook until the sugar is melted and smells caramelized, 10 minutes.
Immediately whisk in the cream and milk mixture (the mixture will steam and the butterscotch will seize, but it will become smooth again with continued whisking).
Bring the mixture to a boil, then turn heat to low.
In a medium bowl, whisk the egg, egg yolks, and cornstarch. Add 1 cup of the hot butterscotch mixture to the egg mixture, whisking constantly. Whisk egg mixture back into the remaining butterscotch.
Bring to a boil, whisking constantly, until the custard is very thick, about 2 minutes. Be careful not to scorch the bottom of the mixture and custard thickens.
Remove from the heat and whisk in the butter and vanilla. At this stage you can either use a blending wand/stick tp puree to smooth OR strain the custard through a fine mesh strainer to remove any lumps. Divide among eight 6-ounce ramekins, 7 ounce custard jars or serving bowls. I use these Mini Tulip Jelly Jar with Glass Lids.
Allow to cool. Cover with plastic wrap and refrigerate until completely chilled, 2-3 hours.