If you use salted cod, you know you need to desalt it first. Soaking it in water at least 12 hours, changing the water at least twice should suffice. Drain it in a colander and set aside.
Place the cod in a bowl with the milk and heat it in the microwave, just 2 or 3 minutes on high. Drain the fish and keep the milk for later. Leave to cool, remove the skin and bones and flake it. Set aside.
Peel the garlic and mash it. Pour 6 tablespoons of the olive oil in a skillet and heat. Add the garlic and stir-fry lightly on low heat, don't let it brown.
Then, while keeping the heat low, add the fish and stir continuously with a wooden spoon, mashing and mixing, until all the oil is absorbed. At this point you can use a hand food processor to make the purée smoother, if you have one.
From then on, start adding the rest of the olive oil (previously heated) and the reserved milk (also warm) little by little, one spoonful of olive oil per half spoonful of milk, alway stirring (or mixing on very low speed) and adding the next spoonful only when the previous one has been absorbed by the mixture.
Recipe by Recetas caseras con fotos paso a paso de Miriam García at https://invitadoinvierno.com/school-of-tapas-catalan-cod-brandada/