Heat the oven to 200 C / 400 F. Lightly oil a 9x13-inch / 33x23cm baking dish.
Slice the potatoes, zucchini, eggplant, onion, and tomatoes into rounds about 1 cm / half inch thick.
In a large mixing bowl, whisk together the olive oil, tomato paste, water, minced garlic, oregano, salt, and pepper until the tomato paste breaks up.
Add the sliced potatoes, zucchini, eggplant, onion, and tomatoes to the bowl. Toss gently with your hands until every slice is coated in the sauce.
Arrange the vegetables in the baking dish, overlapping the slices slightly so they stand upright or lean against each other. Pour any sauce left in the bowl over the top.
Cover the dish tightly with foil and bake for 40 minutes.
Remove the foil and bake for another 20 to 25 minutes, until the vegetables are fork-tender and the tops are lightly browned at the edges.
Remove from the oven and let the dish sit for 5 to 10 minutes so the sauce thickens slightly.
Scatter the chopped parsley over the top and serve warm or at room temperature.