Preheat the oven to 400 degrees F. Spray a rimmed baking sheet with nonstick cooking spray.
Spray the cut sides of the squash with nonstick cooking spray and season with salt and pepper. Place cut-side down on the prepared baking sheet. Roast in the oven until fork tender, about 40 minutes. Remove from the oven and let cool. Increase the oven temperature to 450 degrees F.
Toss the broccoli with the olive oil on a rimmed baking sheet. Season with salt and pepper and roast in the oven until tender, about 10 minutes. Remove from the oven and switch the oven to broil.
Bring a large pot of salted water to a boil over high heat. Add the macaroni and cauliflower and cook until both are tender, 6 to 8 minutes. Drain then transfer to a large bowl.
Meanwhile, melt the butter in a small saucepan. Pour into a small heatproof bowl; add the panko, Parmesan and thyme. Stir to combine and set aside.
Pour the vegetable broth into the same small saucepan and warm over medium heat. Transfer to a blender. Scoop the squash flesh into the blender. Add the Cheddar, feta, yogurt, paprika, 1 teaspoon salt and 1/4 teaspoon coarsely ground black pepper. Carefully blend until smooth. Pour over the macaroni and cauliflower in the large bowl.
Add the roasted broccoli to the large bowl and toss with the sauce, pasta and cauliflower until thoroughly coated. Transfer to a 9-by-13-inch baking dish, cover with the breadcrumbs and broil until browned, about 10 minutes.