Preheat the oven to 350°F and lightly grease a 2-quart baking dish.
Cook the frozen butternut squash according to the package directions until very tender. Mash until smooth, then measure out 2/3 cup and set aside.
Bring a large pot of salted water to a boil. Add the pasta and cook according to the minimum cooking time listed on the package, just until al dente. Drain the pasta and set aside.
Combine the cheddar, Gouda, and Parmesan cheeses. Reserve about 3/4 cup of the combined cheese for topping the mac and cheese before baking.
Melt the butter in a large saucepan or Dutch oven over medium heat. Add the flour and whisk continuously for about 1–2 minutes, until smooth and lightly bubbling.
Slowly pour in the milk while whisking constantly. Continue cooking over medium heat for about 3–5 minutes, stirring frequently, until the sauce has thickened enough to lightly coat the back of a spoon.
Stir the mashed butternut squash into the sauce until smooth and completely combined.
Reduce the heat to low and gradually add the remaining cheddar, Gouda, and Parmesan. Stir until the cheeses are completely melted and the butternut squash cheese sauce is smooth and creamy.
Stir in the salt, nutmeg, black pepper, and hot sauce, if using. Taste and adjust the seasoning as needed.
Add the cooked pasta to the butternut squash cheese sauce and stir gently until the pasta is evenly coated.
Transfer the butternut squash mac and cheese to the prepared baking dish and spread it into an even layer. Cover the baking dish with aluminum foil and bake for 20 minutes.
Remove the foil and sprinkle the reserved cheese evenly over the top. Return the mac and cheese to the oven and bake uncovered for another 10–15 minutes, or until the cheese is melted and the sauce is bubbling around the edges.
Remove from the oven and let the butternut squash mac and cheese rest for about 5 minutes before serving.