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Preheat oven to 375F. Spray a 13x9-inch baking dish with oil.
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Bring butternut squash ans chicken broth to a boil over medium-high heat. Reduce to medium and simmer until squash is fork tender, about 25 minutes.
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Transfer the hot mixture to a blender and add milk, garlic, Greek yogurt, salt, and pepper. Blend until smooth. Transfer to a large mixing bowl and stir in Swiss cheese and 1 cup Parmesan cheese.
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Cook pasta according to package directions and drain well. Stir into the squash mixture. Pour pasta into the prepared baking pan.
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In a small bowl, stir together remaining ¼ cup Parmesan cheese and the bread crumbs. Top the pasta with this mixture and dot with butter.
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Bake in preheated oven for 25 minutes or until bubbly. Serve hot.