Add diced squash to a steamer basket set over simmering water. Cover and steam for 10-12 minutes, or until fork-tender.
Meanwhile, bring a large pot of salted water to a boil. Cook the macaroni 1 minute less than the package directions for an al dente texture. Drain and set aside.
In a blender or food processor, combine the steamed squash, milk, melted butter, salt, pepper, nutmeg, and paprika. Blend until smooth and creamy.
Pour the blended sauce into a large pot (you can reuse the pasta pot after draining). Set over medium-low heat and whisk in cheddar, mozzarella, and Parmesan until melted and smooth.
Add the drained pasta to the sauce and stir until evenly coated. The mixture should be rich, creamy, and thick.
Transfer the mac and cheese to a 9x13-inch baking dish. In a small bowl, combine breadcrumbs, melted butter, salt, pepper, and thyme. Sprinkle evenly over the top.
Bake at 375℉ for 20-25 minutes, until bubbling around the edges and the topping is crisp and golden. Let rest for 5 minutes before serving.