Cut soaked baccala into 2-inch squares and check for any bones.

In a 12-inch frying pan, heat olive oil and butter over medium heat. Add onions, anchovies and cinnamon, and cook until onions are very soft but have not browned, 10 to 12 minutes. Add baccala pieces, wine, and milk and bring to a boil. Lower heat to simmer and cook 1 hour, adding more milk if mixture becomes dry. Add chopped parsley, check for seasoning, and serve with soft polenta.

In a 3-quart saucepan, heat water and salt until boiling. Drizzle in polenta in a thin stream, whisking constantly, until all polenta is incorporated and mixture begins to thicken. Switch to a wooden spoon, pull off heat, and continue to stir until thick as paste.

Stir in the cheese and continue to stir until it is melted and incorporated.