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.

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.