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.