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Prepare pasta according to package directions
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While the pasta is cooking place a large skillet over medium high heat with olive oil. Add the onion and peppers to the skillet cover with a lid and cook, stirring occasionally, until very tender and onions are translucent.
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While the onions and peppers are cooking melt butter in a medium sauce pan over medium high heat then sprinkle flour over the top. Allow it cook for 60 seconds and then slowly whisk milk to the roux allow it to come up to a bubble and thickening.
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Remove the sauce pan from heat and stir in garlic, red pepper flakes, salt, pepper and cheese and set it aside.
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In the skillet add beef broth and roast beef then cooked until warmed through.
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Drain pasta and return to pot. Finally combine the beef, onions and pepper and cheese sauce into the pasta. Garnish with chopped chives if desired.