Prepare the vegetables and preheat the oven to 400 degrees F (200 C).
In a large bowl, combine the potatoes, zucchini, 1 tablespoon oregano, ½ cup chopped parsley, 1 teaspoon rosemary, ½ a teaspoon black pepper, and ½ teaspoon salt.
In another large bowl, combine the tomato sauce, fresh tomatoes, garlic, the rest of the oregano, salt, parsley, and celery. Stir to combine.
Add half the sauce to the bottom of a Dutch oven or large baking dish (round if you have it). Arrange the vegetables in rows, starting with the potatoes and zucchini, adding the carrot and pepper slices, then more potato and zucchini, and red onions, and repeat the process.
Working in a circle, tightly fill the pan with the veggies, then spread the sauce over the vegetables. Cover the dish and bake for 45 minutes. Remove the covering and continue baking for another 30 -40 minutes until the vegetables are very tender.
Remove the dish from the oven and let the Briam sit for a few minutes.
Serve warm or at room temperature with plenty of fresh bread or rice.
Notes
The longer you cook briam uncovered, the more the sauce will thicken.
I used a 13-inch round baking dish for this recipe.