In a small bowl, whisk together the egg yolks, egg and cornstarch. Keep this to hand for later.

In a medium saucepan, bring the cream and milk to a simmer. Turn down very low, or off and cover, to keep warm.

In a large saucepan (large enough for the 4-5 cups milk/cream mixture, plus eggs, plus room to whisk), bring the brown sugar, 1/3 cup water and the salt to a boil. Cook, stirring occasionally to keep mixture from scorching, until it reaches 240°F (115°C). Much of the water will boil off by this stage, but you’ll still have a fair amount of low-level bubbling in the mixture. Mine took about 15 minutes to get to that stage. The mixture should smell nutty and caramelized (although note that we’re not technically making caramel, which requires higher heat).

Immediately add the cream mixture into the brown sugar, and bring to a boil while whisking constantly.

Slowly pour one or two ladles-ful of hot cream mixture into the eggs, whisking constantly to properly temper them. Pour the egg mixture back into the pot with the cream. Cook, whisking, for another few minutes, simmering if need be, until thickened.

Strain the mixture into a bowl to sieve out any unmixed solids (most likely the corn starch) then whisk in the butter until smooth. Divide among 8 serving dishes and chill for at least 4 hours until fully set.