In a large nonstick skillet, heat 3 tablespoons EVOO, 3 turns of the pan, over medium to medium-high heat. Add the potatoes and cook, turning occasionally, until tender, 15 to 20 minutes. Season with salt.
While the potatoes are working, place an ovenproof pan in the oven and preheat to 425 degrees . Rub EVOO all over the cod and cook in the pan for 7 minutes; remove from the oven.
While the fish is working, in a saucepan, heat 2 tablespoons EVOO, 2 turns of the pan, over medium heat. Add the onion and garlic and cook until softened, about 8 minutes. Season with salt and pepper. Stir in the tomatoes.
Top the fish with the tomato sauce. Lay the ham slices on top. Roast the fish until cooked through, 8 to 10 minutes.
Fill a medium saucepan with enough water to reach a depth of 1 inch; bring to a boil. Salt the water, add the green beans and cook until crisp-tender, 5 minutes.
Place a bed of green beans on plates. Top with a cod fillet, tomato sauce and ham. Serve with the potatoes and bread.