In a 12 to 14-inch saute pan, heat 2 tablespoons over medium-high heat until hot, but not smoking. Add the onion and anchovies and cook until the anchovies are breaking up, about 5 minutes. Add 1 thinly sliced garlic and continue cooking until the anchovies have dissolved completely, about more 5 minutes.
Meanwhile, remove the skin from the reconstituted codfish, and slice the flesh in half lengthwise. Cut both pieces of fish cross-sectionally into 1-inch pieces.
Place the flour and 2 tablespoons of Parmigiano into separate shallow bowls. Dredge
a piece of fish in the flour, then the cheese
and set aside. Repeat with the remaining pieces of fish
. In a large skillet, heat 2 tablespoons extra-virgin olive oil. Add the fish pieces and the remaining 10 thinly sliced garlic cloves
. Cook the fish until golden, then flip. Add the onion anchovy
mixture and the milk and bring to a boil. Flake the fish with a fork to see if it is cooked. Add 1/2 cup grated cheese and a drizzle
of extra-virgin olive oil
. Divide the hot polenta evenly among 4 warmed bowls. Spoon the hot codfish and sauce over the polenta and serve immediately.