In separate colanders, lightly salt the eggplant, peppers, and zucchini. Drain for 1 hour. Wipe dry without washing.

In a large frying pan, heat about 1/4 in/6 mm of olive oil over medium heat. Lightly cook the onions and garlic until wilted, about 6 to7 minutes. Remove with a slotted spoon and set aside on paper towels to drain.

Replenish the oil in the frying pan if necessary. Add the potato slices and sauté lightly until their edges begin to color. Lightly sauté all the remaining vegetables separately and set aside to drain on paper towels.

Alternatively, if you don't want to fry, you can preheat the oven to 350F/170C, oil several baking sheets and spread each group of vegetables on individual sheets, brushing them with additional olive oil. Bake for about 15 - 20 minutes, turning once, to soften and color very lightly.

Next, layer the vegetables in a clay or ovenproof glass casserole: Pour about 1/4 cup/60 ml of olive oil into a large, wide pot or Dutch oven. Spoon two tablespoons of the grated tomato and then two tablespoons of the onion-garlic mixture over the bottom. Strew a layer of potatoes and sprinkle with a little salt, pepper and dried oregano. Next, add a little more tomato, onion-garlic, and a layer of eggplant. Press down lightly with the back of a large serving spoon. Sprinkle with a little salt, pepper and dried oregano, then strew a few of the cooked peppers on top. Then, layer the zucchini, and more of the tomato and onion-garlic-salt-pepper-oregano. Press down. Repeat the layering and pressing down, finishing with a layer of eggplant and some tomato-onion-garlic. Drizzle 1/4 cup of olive oil over the top.

Bake at 350F/170C for about 45 minutes to one hour, or until the vegetables are very soft and lightly caramelized. Remove, cool slightly and serve.