0 Preheat the oven to 450°F with racks in the upper and lower thirds.
1 Trim the ends off the squash and peel it. Slice the neck lengthwise into 1/4-inch planks. Halve the bulb, scoop out the seeds, then slice crosswise into 1/4-inch pieces.
2 Place the planks 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, then arrange in a single layer on a baking sheet.
3 Add the remaining sliced squash 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, then arrange in a single layer on a second baking sheet. Transfer both pans to the oven and roast, rotating top to bottom halfway through, until the squash is tender and beginning to brown, 15 to 20 minutes.
5 Meanwhile, heat a large skillet over medium heat. Add the garlic, red pepper flakes, and 1 teaspoon of the oil and cook, stirring, until fragrant, about 1 minute. Add a few handfuls of spinach and the remaining 1/2 teaspoon salt and cook, stirring and adding the rest of the spinach in handfuls, until it's almost completely wilted, 1 to 2 minutes.
6 Transfer to a strainer and press firmly to remove excess liquid, then transfer to the now-empty bowl and cut into pieces with kitchen scissors. Add 2 cups of the cottage cheese, 1 cup of the mozzarella, and several grinds black pepper and stir to combine. Set aside.
7 Add the milk, nutmeg, remaining 1 cup cottage cheese, 1 ounce of the Parmesan cheese, and a pinch each salt and pepper to a personal-sized high speed blender. Blend until smooth.
8 In a small bowl, stir together the breadcrumbs, remaining 1 ounce Parmesan, and remaining 2 teaspoons oil.
9 Combine the roasted squash onto one sheet pan. Pour the white sauce onto the now-empty pan, spreading it to the edges. Arrange all the squash pieces over top (they should mostly fit in one layer, but it's okay if they overlap slightly). Dollop on the spinach-cottage cheese mixture, followed by the pesto (you'll be tempted to add more, but a little goes a long way, and we don't want the final dish to be oily).
11 Sprinkle the remaining 1/2 cup mozzarella evenly over the sheet pan, followed by the breadcrumb mixture. (Be generous around the edges to get them extra crispy).
12 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.
13 Top with fresh basil, then either slice into 6 large rectangles or 12 smaller squares. Pair with a leafy green salad or crusty bread.
