Preheat the oven to 425°F (220°C).

Make the Meat Sauce: Heat the olive oil in a large skillet over medium heat. Add the onion and cook until soft and lightly golden, about 8 minutes.

Stir in the garlic and cook for 30 seconds.

Add the ground beef and cook until browned, breaking it up with a spoon as it cooks.

Stir in the tomato paste and cook for 2 minutes.

Add the crushed tomatoes, water, oregano, cinnamon, cloves, bay leaves, crushed red pepper flakes, sugar if needed, salt, and black pepper. Simmer uncovered for 20 to 25 minutes, or until the sauce has thickened. Remove the bay leaves and stir in the parsley.

Prepare the Veggies: Meanwhile, slice the potatoes, zucchini, eggplant, peppers, onion, and mushrooms into very thin slices using a mandoline or sharp knife.

Bring a pot of salted water to a boil. Cook the potato slices for 3 to 4 minutes, just until slightly tender. Drain well.

Assemble the Dish: Spread the meat sauce evenly into the bottom of a 9x13-inch baking dish.

Arrange the vegetables in overlapping rows or circles over the meat sauce, alternating the colors for a beautiful presentation.

Combine the olive oil, rosemary, oregano, garlic, salt, and black pepper. Brush the herb oil generously over all of the vegetables.

Cover tightly with foil and bake for 45 minutes.

Remove the foil and sprinkle the shredded cheese evenly over the vegetables.

Increase the oven temperature to 450°F (230°C) and continue baking for 15 to 20 minutes, or until the vegetables are tender, the cheese is golden, and the sauce is bubbling around the edges.

Remove from the oven and sprinkle with the feta cheese, parsley, and fresh basil.

Allow the briam to rest for at least 15 minutes before serving.