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1
Bring a large pot of lightly salted water to a boil. Cook elbow macaroni in the boiling water, stirring occasionally, until tender yet firm to the bite, about 8 minutes. Drain and return to the pot.
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2
Place sweet potatoes into a large pot and cover with salted water; bring to a boil. Reduce heat to medium-low and simmer until tender, about 20 minutes. Drain. Mash with a potato masher.
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3
Heat olive oil in a large skillet over medium heat. Add onion, squash, mushrooms, oregano, rosemary, thyme, and pepper; cook and stir until soft, about 10 minutes.
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4
Combine sweet potatoes, onion mixture, and chicken broth in a food processor. Puree until smooth.
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5
Melt butter in the same skillet used to cook the onion mixture. Add flour; cook and stir until a paste forms, about 1 minute. Pour in milk slowly, stirring until smooth. Add 1/3 cup Cheddar cheese; cook over low heat until melted into the sauce, 3 to 5 minutes.
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6
Set oven rack about 6 inches from the heat source and preheat the oven's broiler.
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7
Stir pureed sweet potato-onion mixture into the sauce. Pour sauce over macaroni; mix well. Pour into a 9x13-inch casserole dish. Sprinkle remaining 1/3 cup Cheddar cheese and Parmigiano-Reggiano cheese on top.
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8
Broil in the preheated oven until cheese browns and becomes crisp, 2 to 5 minutes.
