Heat the olive oil in a 5-quart / 4.7 L Dutch oven over medium heat. Add the onions with a pinch of the salt and cook for 6 minutes, stirring now and then, until soft and just starting to turn golden.
Add the garlic and peppers and cook for 4 minutes. Stir in the eggplant and potatoes and cook for 5 minutes, stirring often so everything gets coated in oil. Add the tomato paste and stir for 1 minute.
Add the grated tomatoes, water, oregano, bay leaf, pepper and the rest of the salt. Bring to a gentle simmer, about 3 minutes, then lower the heat to medium-low, partly cover, and cook for 15 minutes.
Stir in the zucchini, partly cover again, and cook for about 15 minutes, stirring gently once or twice. The stew is ready when a fork slides easily into the potatoes and the sauce coats the back of a spoon. If it still looks watery, take off the lid and simmer for 5 more minutes.
Turn off the heat, remove the bay leaf, and stir in the parsley. Let the stew rest uncovered for 10 minutes, then taste and add salt if it needs it. Serve warm.