Spread potatoes, zucchini, and red onions in a 9x13-inch baking dish, or preferably a larger one. Use 2 baking dishes if necessary. Cover with pureed tomatoes, olive oil, parsley. Season with salt and freshly ground pepper. Toss all ingredients together so that the vegetables are evenly coated.
Bake in the preheated oven, stirring after 1 hour, until vegetables are tender and moisture has evaporated, about 90 minutes. Cool slightly before serving, or serve at room temperature.
Notes
You can "puree" the tomato by cutting them in half and grating them on a large box grater, leaving the skin behind.
Don't be afraid of salt and pepper with this dish. Be liberal for best results. Start out as you normally would, and you can always add more seasoning when you check after the 1-hour mark!
If vegetables are too dry in step 3, add a few tablespoons hot water. There should be no water left in the end, however.