Place the cubed butternut squash in a microwave-safe bowl with 2 tablespoons of water. Cover and microwave for 6 to 8 minutes until very fork-tender. Drain and mash with a fork until mostly smooth, leaving a few chunks for texture.

Bring a large pot of well-salted water to a boil. Cook the pasta according to package directions until al dente. Drain and set aside.

Preheat the oven to 375°F and grease a 9x13-inch baking dish. In a large saucepan, melt 2 tablespoons of butter over medium heat. Sprinkle in the flour and whisk for 1 minute to cook the raw flour taste. Slowly whisk in the warmed milk and broth, a little at a time, to keep the sauce smooth.

Bring the mixture to a gentle simmer and whisk often for 4 to 5 minutes until it thickens enough to coat the back of a spoon. Whisk in the mashed squash, nutmeg, salt, and pepper until smooth. Remove from heat and stir in the cheddar, Gruyere, and half of the Parmesan until melted.

Add the cooked pasta to the cheese sauce and stir until every piece is coated. Transfer to the prepared baking dish. Melt the remaining 1 tablespoon of butter and toss with breadcrumbs and remaining Parmesan. Sprinkle evenly over the top.

Bake uncovered for 20 to 25 minutes until the edges are bubbling and the top is deep golden brown. Let it rest for 5 minutes before serving. Garnish with chopped sage.