0 Heat the oven to 450°F with racks in upper and lower thirds.
1 Trim the ends off the eggplant. Slice in half crosswise, then lengthwise into 1/4-inch thick slabs. Place in a large bowl, drizzle with 1 tablespoon of the oil, and season with 1/2 teaspoon salt and several grinds black pepper. Toss to coat and arrange in a single layer on a baking sheet.
2 Trim the ends off the zucchini and/or yellow squash and prepare the same way as the eggplant (slice in half crosswise, then lengthwise into slabs). Place in the now-empty bowl. Trim and de-seed the bell pepper, slice into 1 1/2-inch slabs, and add to the bowl. Drizzle with 1 tablespoon of the oil and season with 1/2 teaspoon salt and several grinds black pepper. Toss to coat and arrange in a single layer on a second baking sheet.
3 Transfer the baking sheets to the oven and roast, rotating top to bottom halfway through, until the veggies are knife-tender, 10 to 12 minutes.
4 Meanwhile, in that same large bowl, combine the cottage cheese, basil, red pepper flakes, 1 1/2 cups of the mozzarella, a pinch of salt, and several grinds black pepper.
5 In a separate smaller bowl, stir together the Parmesan, breadcrumbs, and remaining 1 tablespoon oil.
6 Combine the roasted veggies onto one sheet pan. On the now-empty sheet pan, spread 2 cups of the marinara sauce all the way to the edges. Arrange all of the veggie slices over top (they should mostly fit in one layer, but it’s okay if they overlap slightly).
7 Lay the corn cob flat on a cutting board. Slice off a strip of corn, rotate so the flat side is on the cutting board, and continue until all of the kernels are removed. Sprinkle over the sheet pan.
8 Dollop on the cottage cheese mixture, followed by the remaining sauce. (You can either drizzle it over everything or add it in spoonfuls).
9 Sprinkle the remaining 1/2 cup mozzarella evenly over the sheet pan, followed by the breadcrumb mixture. (Be generous around the edges of the sheet pan to get them extra crispy).
10 Adjust one of the oven racks to the center position. Bake (still at 450°F) until the sauce is bubbling and the cheese is browned in spots, 20 to 25 minutes. Let sit at least 5 minutes to firm up slightly and make it easier to slice.
12 Top with fresh basil, then either slice into 6 large rectangles or 12 smaller squares. Pair with a leafy green salad, crusty bread, or a side of pasta.
