While the sauce is cooking, prepare the vegetables: Peel the potatoes and tomatoes. Cut the zucchini, squash, tomatoes, and eggplant into thin, about 1/4 inch (5mm) slices, cut the potatoes a little thinner (you can use a sharp knife or a mandoline). Make sure you slice the potatoes more thinly than the rest of the vegetables.
Preheat the oven to 425°F / 220°C / Gas Mark 7, no fan.
Spoon the sauce into the baking dish, even out its surface. Note: if you're using a rectangular 9x13 inch (23cmx33cm) casserole dish use the whole amount of the sauce, if you're using an oval 9x13 inch (23cmx33cm) casserole dish, add a little less sauce - about 1/2-2/3 cup less sauce (you can use it for another recipe or bake it with the leftover vegetables that won't fit in your baking dish).
Arrange the vegetables in the baking dish in an alternating layered pattern from the outer edge to the inside until the entire baking dish is filled.
Sprinkle salt, pepper, and some more Herbes de Provence over the vegetables. Pour a small amount of olive oil over them.
Bake for 45 minutes (uncovered) until the sauce is bubbly and the vegetables are browned (if the vegetables are not browned you can turn on the fan or move the baking dish under the most upper rack / under the broiler and bake briefly until the edges of the vegetables are browned).
Sprinkle grated cheese over the vegetables and bake under the broiler (or turn on the fan) for about 5-10 minutes until the cheese is melted and slightly golden.
Take the casserole out of the oven and leave to rest for about 15 minutes.
Serve and enjoy!