Gather all ingredients. Preheat the oven to 400 degrees F (200 degrees C).
Spread potatoes, zucchini, and red onions in an extra-large baking dish (9x13-inch or larger, or 2 baking dishes).
Cover with puréed tomatoes, olive oil, and parsley; season liberally with sea salt and pepper. Toss until vegetables are evenly coated.
Bake in the preheated oven for 1 hour. Stir gently, then continue baking until vegetables are tender and moisture has evaporated, about 30 minutes more.
Cool briam slightly before serving or serve at room temperature.