Preheat the oven to 400 degrees.
Rinse and trim the stems off of the beets, zucchini and yellow squash. Peel the beets. Scrub the sweet potato very well, but you don’t have to peel it unless you dislike the skin. Then slice each of the veggies into very thin rounds, approximately ⅛ inch slices. Set these all aside.
In a medium to large baking dish, grease the bottom and sides with 1 tablespoon of olive oil. Pour the can of diced tomatoes into the dish, allowing it to evenly coat the bottom. Sprinkle the goat cheese or ricotta, garlic and basil on top of the diced tomatoes. Season with salt and pepper.
Alternating veggies, stack them upright around the outside of the baking dish, then fill in the center. Drizzle with the remaining tablespoon of olive oil and season with salt and pepper.
Cover with aluminum foil and bake for 45 minutes.
While it is baking, combine the breadcrumbs and shredded parmesan cheese in a small bowl. Drizzle with 2 tablespoons of olive oil and stir to combine well. If the bread crumbs are a bit dry, you may need a little more oil. Just be sure that it isn’t dripping with oil. The goal is for it to look damp, not soaked.
After the veggies have baked for 45 minutes, carefully remove the aluminum foil and sprinkle the breadcrumb mixture on top of the veggies. Return to the oven to bake for another 15 minutes or until the topping is browned and crisp.