Fill a large bowl half way with ice. Pour cold water over the ice so that the bowl is no more than ⅔ high. Place a clean bowl on top of the water bath. Place a strainer over the empty bowl.
Caramel: Pour the sugar into a medium (3 quart) pot. Carefully pour the water over the sugar, trying not to let any of the sugar ride up the sides of the pot. Carefully stir, just to hydrate all the sugar. If any sugar crystals ride up the sides of the pot, use a pastry brush dipped in water and run it along the sides of the pot without allowing the bottom of the pastry brush to touch the mixture. This will cause any sugar crystals to fall into the rest of the mixture.
On a medium-high heat, cook the sugar mixture. Swirl the pot or stir occasionally, using the wet pastry brush to wipe any sugar crystals that run up the sides of the pot. Once the mixture starts to boil, do not stir the mixture again. Just carefully swirl the pot. Cook until amber/light brown/dark red in color. It should be lightly smoking. It will go from caramel to burnt quickly, so pay close attention.
Ice Cream Base: When you first put the heat on under the sugar and water for the caramel, in a smaller pot on high, heat the milk, heavy cream and salt just until it comes to a boil. Remove from the heat and stir in the vanilla, keeping the mixture in the pot.
As soon as the caramel is cooked, turn the flame off and carefully and slowly, with a wooden spoon, stir in the heated milk/cream mixture, just a little at a time. The entire mixture will bubble up violently (so be careful and add the milk/cream in small batches) and the caramel may seize. On medium heat, heat the mixture, stirring frequently, until the caramel is melted and the entire mixture is combined and smooth and comes to a simmer. Turn the heat off and let it sit for a minute or two.
Meanwhile, in a small bowl, whisk the yolks with the remaining 50 g. (¼ cup) of sugar until it is pale yellow, thick, and forms a ribbon on itself.
With the bowl holding the egg/sugar mixture secure on the counter (if no one is around to hold it, place it on a rubber mat or wet a dishtowel and wrap it around the base of the bowl), slowly pour half the heated liquid mixture into the eggs, whisking constantly. Once fully incorporated, pour the contents of the bowl back into the pot. Over a medium-low heat, stir the mixture constantly with a wooden spoon until it reaches 185°F or a line holds when you drag your finger across the back of the wooden spoon. (It should only take a minute or two reach the correct temperature.)
Immediately remove the pot from the heat and pour the cooked mixture through the strainer into the empty bowl sitting in the ice water bath. Stir the mixture as it sits in the ice bath every 2 to 3 minutes until the mixture has completely cooled. This usually takes about 10 minutes.
Pour into a container. Cover with plastic wrap directly over (touching) the mixture. Cover and place in refrigerator for 4-24 hours.
Follow your ice cream manufacturer’s directions to churn the ice cream. Transfer the ice cream to a freezer container. Cover with a piece of parchment paper or plastic wrap directly on the surface. Cover container and freeze.