Place the zucchini in layers in a large colander, salting lightly between each layer. Place in the sink or inside a larger bowl. Place a kitchen towel over the zucchini and a weight, such as cans, over the towel to press down and drain the zucchini. Let it stand for at least an hour and up to eight. Pat dry.

Lightly oil a large ovenproof glass or ceramic baking pan. Place all the vegetables except the tomatoes in a large mixing bowl and toss with the herbs, olive oil and a generous sprinkling of coarse salt and pepper.

Preheat the oven to 350F/ 170C. Place all the vegetables except the tomatoes in alternating pieces in neat rows, one snugly next to the other. Using a rubber spatula, scrape out any oil and herbs or other liquid from the mixing bowl and pour over the vegetables. Strew the chopped tomatoes over the surface of the vegetable rows. If desired, even though this sounds unbelievable to most American cooks, drizzle a little more olive oil over the top!

Cover with a piece of wax or parchment paper, then aluminum foil and bake in the middle of the oven for about 40 minutes, or until the vegetables are soft but the potatoes still likely to be al dente. Remove the paper and foil and continue baking the briam until most of the pan liquid has evaporated and the surface of the vegetables is lightly charred. I sometimes turn on the broiler to achieve this, and you can, too, if the potatoes are cooked to the point you like.

Remove, cool slightly, and serve, drizzled with more extra virgin Greek olive oil. The briam is great at room temperature, too, and it pairs beautifully with great bread and a wedge of feta cheese.