Put the sugar into a heavy duty pot (I used my round Le Creuset) and set it over medium-high heat. Let it sit until it starts to melt and liquefy in spots. (This will depend on your stovetop.) Continue to cook, stirring occasionally with something heatproof, until it melts completely, turns deep golden and just barely begins to smoke. If you get nervous, don't even wait for the smoking part.
Carefully (it will steam) pour in the cream and stir - the melted sugar will seize up and harden - don't worry about it. Stir to dissolve the sugar caramel. Stir in the milk and salt.
Beat the egg yolks with a fork in a small bowl. Slowly pour some of the hot caramel into the yolks, stirring briskly, then whisk the egg yolk mixture back into the caramel in the pot. Cook over medium heat until it bubbles and thickens enough to coat the back of a spoon - if you draw your finger through, it should leave a trail.
Pour the custard through a sieve into a bowl. (I tend to skip this step, but it takes about 20 seconds and is well worth getting any rogue bits of cooked egg out of your custard.) Put the bowl out into a snowdrift, or set it on a bowl of ice, or slide it into the fridge (put a piece of parchment or plastic wrap on the surface to prevent a skin forming), and cool until well chilled.
Stir in the espresso and freeze in your ice cream machine.
Call me and I'll come share it with you.