Rinse salt cod thoroughly and place in large container with enough water to cover generously. Let soak 7 to 8 hours or overnight, changing water once or twice. After soaking, cod should feel plump to the touch. Drain well and cut into 1-inch pieces.
Place potatoes in a large pot with enough water to cover generously. Bring to a boil over high heat, reduce heat to medium. Cook, partially covered, until they are fork-tender, 30 to 40 minutes.
Meanwhile, in large skillet, warm olive oil over medium-high heat. Add garlic, onion, bay leaf, and tomatoes. Sauté and stir until tomatoes have broken up, 3 to 4 minutes. Add cod pieces and cook over medium heat 3 to 4 minutes, stirring often. Add raisins and cover. Cook over medium heat 15 minutes, stirring once. Cod should now be well broken up and have begun shredding. Remove bay leaf and reduce heat to low. Stir in milk slowly to prevent curdling. Cook uncovered another 4 to 5 minutes.
Drain potatoes and place on plates. Serve stew over potatoes and sprinkle with Parmesan cheese.