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While the pasta is boiling, heat the butter in a medium saucepan, then add the onions and garlic.
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Cook onions and garlic until soft, around 2-3 minutes, then add flour and stir to coat
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Add broth and milk to the saucepan and, whisking constantly, bring to a slow boil until mixture thickens.
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Remove from heat and add the cheeses, stirring to melt.
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Pour the sauce over the pasta mixture and stir well to combine.
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Place pasta and sauce mixture into a casserole dish or cast iron pan, and sprinkle with parmesan.
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Bake at 350F for 30 minutes.