* (If using red beets, remember that they will bleed.)
Preheat oven to 375°F. Slice the vegetables no more than ¼ inch thick. (A mandoline or food processor is really useful for this dish.)
Spray an 8- by 12-inch glass baking dish (or similar baking dish) with cooking spray. Arrange about ¼ of the vegetable slices in the dish, overlapping them slightly; season with salt and pepper. Add remaining vegetable slices — about ¼ of the slices at a time, seasoning each layer. Pour the broth over and around the vegetables
Cover tightly with foil and bake for 1 hour, until the vegetables are almost tender when pierced. Remove the foil and pour the cream over the gratin. Bake for about 30 minutes longer, until the liquid has thickened.
Preheat the broiler. Mix the panko with the oil and season with salt and pepper; add Parmesan cheese if using, sprinkle mixture over the gratin. Broil 3 inches from the heat for 2 minutes, until golden, rotating for even browning. Let the gratin stand for 10 minutes, then serve