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To make the sauce, melt butter, onion and garlic over medium low heat. Cook until onion is softened, about 3 minutes. Add flour and cook for 1-2 minutes.
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Reduce heat to low. Combine milk and broth. Add a small amount at a time whisking to thicken. The mixture will become very thick, continue adding a little bit of liquid at a time whisking until smooth.
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Once all of the liquid has been added, bring to a boil over medium heat while continuing to whisk. Stir in salt and pepper and let boil 1 minute.